Copy the proof on paper, mark the givens in the diagram, and fill in the blanks to complete the proof.

This is the actual answer:

The missing values are PU, PU ≅ PU, UR, PR, and Triangle RUP by applying Corresponding parts of congruent triangles are congruent.

The measurements of the sides and angles of two or more triangles determine their congruence. A triangle's size is determined by its three sides, and its shape is determined by its three angles. If the pairs of corresponding sides and angles of two triangles are equal, they are said to be congruent.

We have:

As we can see in the diagram,

First, we will draw PU

PU is the common side for both the triangles

PU ≅ PU (reflexive property)

UO ≅ UR (given)

PO ≅ PR (given)

By the property of SIde-Side-Side

The triangle OUP  ≅ Triangle RUP

By Corresponding parts of congruent triangles are congruent:

Angle O ≅ Angle R (proved)

Thus, the missing values are PU, PU ≅ PU, UR, PR, and Triangle RUP by applying Corresponding parts of congruent triangles are congruent.

Learn more about the congruence in the triangles here:

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