1
QuizMultiple Choice

Triangle Similarity — Test

Question 1 • TPS EdX Geometry

Which would prove that triangle cap A cap b cap c approximates triangle cap x cap y cap z ? Choose two correct answers.

Answer
A
the fraction with numerator cap b cap A and denominator cap y cap x is equal to the fraction with numerator cap b cap c and denominator cap y cap z comma angle cap c is congruent to angle cap z
B
the fraction with numerator cap b cap A and denominator cap y cap x is equal to the fraction with numerator cap A cap c and denominator cap y cap z is equal to the fraction with numerator cap b cap c and denominator cap x cap z
C
the fraction with numerator cap A cap c and denominator cap x cap z is equal to the fraction with numerator cap b cap A and denominator cap y cap x comma angle cap A is congruent to angle cap x
D
the fraction with numerator cap b cap A and denominator cap y cap x is equal to the fraction with numerator cap b cap c and denominator cap y cap z is equal to the fraction with numerator cap A cap c and denominator cap x cap z
E
the fraction with numerator cap b cap c and denominator cap x cap y is equal to the fraction with numerator cap b cap A and denominator cap z cap x comma angle cap c is congruent to angle cap x

Explanation

Choice A gives three pairs of corresponding sides in the same ratio: AB/XY = BC/YZ = AC/XZ. That proves the triangles are similar by SSS. Choice E gives two pairs of corresponding sides in the same ratio, AB/XY = AC/XZ, and the included angles A and X are congruent, so it proves similarity by SAS.

AI-written and checked against the verified answer.

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