Given segment AC bisects angle BAD, angle B is congruent to angle D. Prove segment BC is congruent to segment CD

Answers

Answer 1

The proof that BC is congruent to segment CD, where  AC bisects angle BAD, angle B is congruent to angle D is given below:

AC bisects ∠BAD, => ∠BAC=∠CAD .................... 1

thus in ΔABC and ΔADC,  ∠ABC=∠ADC (given),

                                      ∠BAC=∠CAD     from 1)],

AC (opposite side side of ∠ABC) = AC (opposite side side of ∠ADC), the common side between ΔABC and ΔADC

Hence,  

by AAS axiom, ΔABC ≅ ΔADC,

Therefore,  BC (opposite side side of ∠BAC) = DC (opposite side side of ∠CAD),  since (1)

Thus, BC=DC proved.

What is proof?

A mathematical proof is an inductive argument for a mathematical assertion that demonstrates that the provided assumptions logically ensure the conclusion.

A proof is an argument that you use to persuade your readers that a mathematical assertion is correct. It might be a calculation, a verbal debate, or a combination of the two. Proof writing, as opposed to computational math problems, necessitates higher attention on mathematical precision, organization, and communication.

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Related Questions

in 2016, astronomers measured the farthest galaxy in the universe found to date, gn-z11. this involved the use of law.

Answers

The Doppler effect was used to estimate the velocity of galaxies, and according to scientists, galaxies that are farthest from the universe's center travel faster.

Describe the Doppler effect with an example.

The apparent change in wave frequency brought on by the displacement of such a wave source is known as the Doppler effect. When the wave source is coming closer and when it is moving away, the perceived frequency changes. The Doppler effect describes why humans hear a passing siren's sound changing in pitch.

What is the Doppler effect's alternate name?

The Doppler shift is another name for the Doppler effect. The carrier frequency is less than the origin frequency if the source and observer are becoming further apart. Red shift is the term used to describe the phenomenon in relation to light waves.

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according to a 2014 report conducted by yale university and george mason university, the majority of the public surveyed in the united states agreed that global warming is occurring, and believed it was caused primarily by human activities.

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According to a 2014 report conducted by yale university and George Mason university, the majority of the public surveyed in the united states agreed that global warming is occurring, and 50% believed it was caused primarily by human activities.

Using fossil fuels like coal and oil has increased the quantity of carbon dioxide in the atmosphere during the last century (CO2). This increase is the consequence of burning coal or oil, which creates CO2 when oxygen and carbon dioxide in the air combine. A rise in greenhouse gas concentrations has been mostly attributed to the clearance of land for industrial, agricultural, and other human endeavors which in turn contributes to Global warming.

The industrial activity on which our modern civilization depends have raised atmospheric carbon dioxide levels by over 50% since 1750. The spike in temperature may be attributed to human activities, according to a distinct isotopic fingerprint that researchers have found in the atmosphere.

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what is the percentage of the west coast compared to canada​

Answers

Answer:

80%

Explanation:

The majority of Canada's population is concentrated in the areas close to the Canada–US border. Its four largest provinces by area (Ontario, Quebec, British Columbia, and Alberta) are also its most populous; together they account for 86.5% of the country's population.

Without the discovery of magnetic reversals recorded on the ocean floor, scientists.

Answers

Without the discovery of magnetic reversals recorded on the ocean floor, scientists could not provide a mechanism for moving continents.

Causes and effects of the invention of magnetic reversal

Scientists don't really know what causes magnetic field reversals, though they have duplicated the phenomenon in laboratory experiments with liquid metals, which would also spontaneously change the direction of their magnetic fields. Some theorists believe that magnetic field reversals could be caused by real events, such as the collision of tectonic plates or the impact of a large meteor or asteroid, but this theory is discounted by others. It is known that leading up to a magnetic reversal, the field strength decreases, and since our current magnetic field strength is now in steady decline, some scientists believe we will see another magnetic reversal in about 2,000 years.

If, as some scientists have suggested, there was a period in which there was no magnetic field at all before the reversal occurred, the effect on the planet is not well understood.

Some theorists suggest that having no magnetic field would expose the Earth's surface to harmful solar radiation that could potentially cause the global extinction of life. However, there are currently no demonstrable statistical correlations in the fossil record to verify this. The last reversal occurred around 780,000 years ago, and there is no evidence to suggest that there was a mass species extinction at that time. Other scientists argue that the magnetic field does not dissipate during a reversal, but only grows weaker temporarily.

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which of the following occurs when the sun, moon, and earth are in alignment (i.e., in opposition or conjunction)?

Answers

Whenever the sun, moonlight, and earth are lined up, the tidal ranges are at their greatest.

How do tidal ranges work?

The term "tidal range" refers to the height difference between high tide and low tide. The rising and lowering of the tide is frequently accompanied by a horizontal water movement. The values after Morgat correction are: 1.50 - 0.10 Equals 1.40 m of low water. 7.10 - 0.40 ≈ 6.70 m is the high tide.

The significance of tidal range.

The seashore is more affected by this phenomenon as the tide range increases. However, the slope of the a beach or even other coastal landform is equally significant since, even in a macro-tidal setting, a steep cliff only offers a minimal difference in the region over which the waves and currents can operate.

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which of these are characteristics of an artesian well?
A. penetrates an unconfined aquifer
B. requires pumping
C. penetrates a confined aquifer
D. does not require pumping

Answers

characteristics of an artesian well are does not require pumping, penetrates a confined aquifer.

What is an artesian aquifer ?

Pressurized aquifer intersecting the surface from which water gushes without being pumped. Water table. Top layer of water in an aquifer.

Why does an artesian well flow without pumping?

A well that has been dug into an aquifer in a place where the pressure below the ground is high enough for the water to rise inside the well is called an artesian well. Sometimes there is enough pressure for the water to rise from the aquifer to the surface of the ground without the use of a pump.

What does an artesian well require?

Simply put, an artesian well is a well that draws water to the surface without the aid of a pump. When the aquifer's positive pressure is high enough, the water rises to the surface. This positive pressure is brought on by an artesian aquifer that is contained between impermeable rocks or clay.

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One dish of Sweden translates into "Sour Herring" and is fermented fish.
O True
O False

Answers

Answer:

the answer is 01110100 01110010 01110101 01100101 . do a tiny bit of work decoding it

Explanation:

one way to treat a dying beach is to dig up sand somewhere and dump it on the beach. what is this likely to accomplish? group of answer choices it causes growth of the beach for the next century, because the sand attracts more sand from the longshore drift. it causes the beach to lose the new sand, but only after many centuries, as the extra sand is very, very slowly washed back to deep water by waves and currents. it causes the sand to pile up under the boardwalk, forcing all the people hiding under there to run up into the sun and do song-and-dance numbers to music from the 1950s. it causes the beach to lose the new sand over the next year or years, as the extra sand is washed back to deep water by waves and currents.

Answers

The excess sand is washed back to water depths by waves and currents, causing the beach to lose the fresh sand over the next year or so.

Sand is moved by waves and currents. To make up for this, we'll have to move a lot of sand. Building beaches from extracted sand can work, but the sand quickly returns to deep water, so the activity must usually be reiterated every year or every few decades to keep the beaches large and sandy.

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T/F work related deaths from large machinery falling objects electric current and explosion are highest in rural western urban southern states

Answers

Answer: Answer:

B. 7 feet

Step-by-step explanation:

Given:

NS = (x + 10) ft

SR = (x + 3) ft

Required:

RS

SOLUTION:

Based in the centroid theorem, the centroid, S will divide the median, line segment NR, into NS and SR, such that NS : SR = 2 : 1.

Therefore:

NS = 2(SR)

x + 10 = 2(x + 3) (substitution)

Solve for x

x + 10 = 2x + 6

Collect like terms

x - 2x = -10 + 6

-x = -4

divide both sides by -1

x = 4

SR = (x + 3) ft (SR is same as RS)

Plug in the value of x

SR = (4 + 3) ft

SR = RS = 7 ft

Answer:

B. 7 feet

Step-by-step explanation:

Given:

NS = (x + 10) ft

SR = (x + 3) ft

Required:

RS

SOLUTION:

Based in the centroid theorem, the centroid, S will divide the median, line segment NR, into NS and SR, such that NS : SR = 2 : 1.

Therefore:

NS = 2(SR)

x + 10 = 2(x + 3) (substitution)

Solve for x

x + 10 = 2x + 6

Collect like terms

x - 2x = -10 + 6

-x = -4

divide both sides by -1

x = 4

SR = (x + 3) ft (SR is same as RS)

Plug in the value of x

SR = (4 + 3) ft

SR = RS = 7 ft

Answer:

B. 7 feet

Step-by-step explanation:

Given:

NS = (x + 10) ft

SR = (x + 3) ft

Required:

RS

SOLUTION:

Based in the centroid theorem, the centroid, S will divide the median, line segment NR, into NS and SR, such that NS : SR = 2 : 1.

Therefore:

NS = 2(SR)

x + 10 = 2(x + 3) (substitution)

Solve for x

x + 10 = 2x + 6

Collect like terms

x - 2x = -10 + 6

-x = -4

divide both sides by -1

x = 4

SR = (x + 3) ft (SR is same as RS)

Plug in the value of x

SR = (4 + 3) ft

SR = RS = 7 ft

Answer:

B. 7 feet

Step-by-step explanation:

Given:

NS = (x + 10) ft

SR = (x + 3) ft

Required:

RS

SOLUTION:

Based in the centroid theorem, the centroid, S will divide the median, line segment NR, into NS and SR, such that NS : SR = 2 : 1.

Therefore:

NS = 2(SR)

x + 10 = 2(x + 3) (substitution)

Solve for x

x + 10 = 2x + 6

Collect like terms

x - 2x = -10 + 6

-x = -4

divide both sides by -1

x = 4

SR = (x + 3) ft (SR is same as RS)

Plug in the value of x

SR = (4 + 3) ft

SR = RS = 7 ft

Answer:

B. 7 feet

Step-by-step explanation:

Given:

NS = (x + 10) ft

SR = (x + 3) ft

Required:

RS

SOLUTION:

Based in the centroid theorem, the centroid, S will divide the median, line segment NR, into NS and SR, such that NS : SR = 2 : 1.

Therefore:

NS = 2(SR)

x + 10 = 2(x + 3) (substitution)

Solve for x

x + 10 = 2x + 6

Collect like terms

x - 2x = -10 + 6

-x = -4

divide both sides by -1

x = 4

SR = (x + 3) ft (SR is same as RS)

Plug in the value of x

SR = (4 + 3) ft

SR = RS = 7 ft

Explanation:

Which of the following biomes has the highest soil nutrient levels? (a) Tropical rainforest, (b) Temperate rainforest, (c) Boreal forest, (d) Woodland/shrubland, (e) Temperate seasonal forest.

Answers

This biome's extremely rapid decomposition is caused by the warm temperature and abundant rainfall, allowing the vegetation to quickly absorb the soil's nutrients and achieve high productivity. Letter (a) is the most appropriate response here.

What do tropical rainforests consist of?

The majority of tropical rainforests can be found in the tropics, between 23.5°N (the Tropic of Cancer) and 23.5°S (the Tropic of Capricorn). Central and South America, western and central Africa, western India, Southeast Asia, the island of New Guinea, and Australia all have tropical rainforests.

Which three main tropical rainforests are there?

There are three regions of the tropical rainforest: Neotropical (South America and Focal America), African (Africa and Madagascar), and Indo-Malaysian (India, Southeast Asia, Australia and the Pacific Islands).

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Underground coal mining is more dangerous and labor extensive compared to _____ mining, so it is also more expensive

Answers

Underground coal mining is more dangerous and labor extensive compared to strip mining, so it is also more expensive.

The process of removing coal from the earth is known as mining. Because of its high energy content, coal has been utilized extensively to produce electricity since the 1880s. Coal is used as a fuel in the steel and cement industries to extract iron from iron ore and to make cement.

Environmental concerns have become more significant since 1970, including the health of workers, the degradation of the environment caused by strip mining and mountaintop removal, air pollution, and the impact of coal burning on global warming. By removing the ground above each coal seam, strip mining exposes the coal. The earth that has to be removed is known as "overburden" and is taken out in broad strips.

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________ describes the range in particle sizes in a detrital sedimentary rock.
A) Sorting B) Cementation C) Size D) Shape

Answers

Answer:

sorting

Explanation:

hope it helps

thanks

Medieval Christian philosophers found problems with which one of the following Aristotelian ideas?
a. The eternity of the universe, the function and existing of the soul, the concept of cause and effect
b. The concept of a finite universe, the relationship between body and soul, the concept of Will and Destiny
c. The concept of an infinite universe (both spatial and temporal), the relationship between body and soul, the concept of action in a distance
d. All these statements are correct
None of these statements is correct

Answers

All the above:

The eternity of the universe, The function and the existing of the soul, The concept of cause and effect.

What are the main features of medieval Christian philosophy?

Early Christian philosophy, especially in the patristic era, had a tendency to be intuitive and mystical and relies less on reasoning and argumentation. Additionally, it places less emphasis on Aristotle's methodical reasoning and more emphasis on the at times mystical beliefs of Plato.

What is Christian aristotelianism?

Aristotle's theory that society develops out of human nature rather than from human vice and corruption was one that Aquinas endorsed. According to him, the state is a naturally occurring institution that comes from the nature of man. Man is a social and political animal by nature, with a predetermined and set aim.

What is Aristotelian method in philosophy?

Aristotle uses reasoning and observation in his natural philosophy to draw broad, causal conclusions. Aristotle, for instance, uses the idea of species to support his factual claims about the purposes and behaviors of particular creatures in his biology.

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