We have an answer to "To determine:To prove: △RST∼△XYZ by the SAS similarity..."

High School
Geometry
High school geometry
Similarity

Mylo O'Moore

Answered question

2020-11-30

To determine:To prove:

△ R S T \sim △ X Y Z

by the SAS similarity theorem.
Given:
The triangles are similar by theorem SAS.

∠ R = ∠ X

(Given)

Answer & Explanation

Raheem Donnelly

Skilled2020-12-01Added 75 answers

Calculation:
SAS theorem for similarity states that the ratios of two sides of one triangle to the corresponding triangle’s two side must be equal. Angle between equal ratios sides of both the triangle must be equal.
In triangle RST and XYZ,

∠ R = ∠ X

(Given)
Ratios of the sides with end R and X must be equal.
Consider the ratios of sides as follows:

\frac{R S}{X Y} = \frac{R T}{X Z}

Hence, theratios of

\frac{R S}{X Y} and \frac{R T}{X Z}

must be equal to prove

△ R S T \sim △ X Y Z

by SAS similarity theorem.

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