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Which of the below is the only correct
similarity statement for the two triangles?

Which of the below is the only correct similarity statement for the two triangles-example-1
User Klathzazt
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3 votes
They are both the same shape but turned different ways
User Spinner
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Based on the image you sent, the only correct similarity statement for the two triangles is: D) △ORA ≅ △GEN

Here's why:

Corresponding sides are proportional:

OR = GE (both sides labeled with a single line segment)

RA = GN (both sides labeled with a single line segment)

OA = EN (both sides labeled with two line segments)

Matching angles:

Angle A in △ORA is congruent to Angle G in △GEN (both marked with a double angle symbol)

Therefore, by the Side-Side-Side (SSS) similarity criterion, △ORA is similar to △GEN.

The other options are incorrect because:

A) △ORA-△NGE: Sharing only side OR and angle A is not enough for similarity.

B) △ORA-△ENG: Sharing only side OA and angle A is not enough for similarity.

C) △ORA-△GNE: Sharing only side GE and angle A is not enough for similarity.

User Waqas Idrees
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