The missing values are PU, PU ≅ PU, UR, PR, and Triangle RUP by applying Corresponding parts of congruent triangles are congruent.
What is congruence in the triangles?
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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