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Copy the problems onto your paper, mark the givens and prove the statements asked.
Given: marked, PQ=8
PR=2x, TU=2z+3, ST=5z
Find: PR and ST

1. PR = 8 units

2. ST = 5 units

Step-by-step explanation:

1. Consider triangles QSP and RSP. In these triangles,

- all right angles are congruent

- reflexive property

- given

So, by SAS postulate (SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent).

Congruent triangles have congruent corresponding parts, then

Given you get

and

2. Consider triangles VST and VUT. In these triangles,

- all right angles are congruent

- reflexive property

- given

So, by AAS postulate (AAS postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent).

Congruent triangles have congruent corresponding parts, then

Given

you get

Then

my guess is

step-by-step explanation: