Which side in the smallest triangle would correspond with RS― in the largest triangle? RS― RQ― QS― None of the sides correspond with RS―

Question: "Which side in the smallest triangle would correspond..."

High School
Geometry
High school geometry
Similarity

Rivka Thorpe

Answered question

2021-08-04

Which side in the smallest triangle would correspond with

\overset{―}{R S}

in the largest triangle?

\overset{―}{R S}

\overset{―}{R Q}

\overset{―}{Q S}

None of the sides correspond with

\overset{―}{R S}

Answer & Explanation

averes8

Skilled2021-08-05Added 92 answers

Step 1
A right-angle triangle with an altitude is given in the problem.
Triangle PSR is the largest triangle and triangle RQS is the smallest triangle.
From the figure,

∠ P S R = ∠ S Q R = 90^{\circ}

(Angle)

∠ S R P = ∠ Q R S

(Angle)
The above equality satisfies the AA similarity theorem. So, the

△ S R P \sim △ Q R S

.
Step 2
From the similarity

△ S R P \sim △ Q R S

,
The side

\overset{―}{R S}

and side

\overset{―}{R Q}

are corresponding to each other.
Thus, the second option is the correct option.

2022-08-25

I think it would be QS

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