Step by step solution to "Given: △GRA △ERT ∠GRAand∠ERT are vertical. RE=2AR RT=2GR..."

High School
Geometry
High school geometry
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glamrockqueen7

Answered question

2021-08-10

Given:

△ G R A

△ E R T

∠ G R A and ∠ E R T

are vertical.

R E = 2 A R

R T = 2 G R

Prove:

△ G R A \sim △ E R T

Answer & Explanation

okomgcae

Skilled2021-08-11Added 93 answers

We are given that $∠ G R A and ∠ E R T$ are vertical, therefore:
$∠ G R A \tilde{=} ∠ T R E$
We are also given that RE=2AR and RT=2GR, so
$\frac{R E}{A R} = \frac{R T}{G R}$
Since two pairs of legs are proportional and their included angles are congruent, it's proven that $△ G A R \sim △ T E R$ by the SAS~Theorem.

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