Question

First determine the missing angle for triangle 1 and triangle 2. Then apply the angle-angle criterion to determine if the two triangles are similar. Choose all that are similar. Triangle 1 – ∠1 = 50°, ∠2 = 30° Triangle 2 – ∠2 = 20°, ∠3 = 100° Triangle 1 – ∠1 = 60°, ∠2 = 20° Triangle 2 – ∠1 = 40°, ∠3 = 100° Triangle 1 – ∠1 = 25°, ∠2 = 115° Triangle 2 – ∠1 = 25°, ∠3 = 40° Triangle 1 – ∠1 = 5°, ∠2 = 15° Triangle 2 – ∠2 = 15°, ∠3 = 160°

Answer 1

• Triangle 1 – ∠1 = 25°, ∠2 = 115° Triangle 2 – ∠1 = 25°, ∠3 = 40°
• Triangle 1 – ∠1 = 5°, ∠2 = 15° Triangle 2 – ∠2 = 15°, ∠3 = 160°

Explanation:

You can save yourself some trouble if you realize that one of the angles in one pair must match one of the angles in the other pair.

This observation eliminates the first two choices.

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Going further, the triangles will be similar if the dissimilar angles together with one of the similar angles totals 180°.

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Triangle 1 – ∠1 = 50°, ∠2 = 30°

Triangle 2 – ∠2 = 20°, ∠3 = 100° . . . . . no angles match

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Triangle 1 – ∠1 = 60°, ∠2 = 20°

Triangle 2 – ∠1 = 40°, ∠3 = 100° . . . . . no angles match

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Triangle 1 – ∠1 = 25°, ∠2 = 115°

Triangle 2 – ∠1 = 25°, ∠3 = 40° . . . . 25° angles match; 25+40+115 = 180

These triangles are similar.

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Triangle 1 – ∠1 = 5°, ∠2 = 15°

Triangle 2 – ∠2 = 15°, ∠3 = 160° . . . . 15° angles match; 15+5+160 = 180

These triangles are similar.