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Alex Ar [27]
3 years ago
9

First determine the missing angle for triangle 1 and triangle 2. Then apply the angle-angle criterion to determine if the two tr

iangles 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°
Mathematics
1 answer:
barxatty [35]3 years ago
7 0

Answer:

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

Step-by-step 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.

__

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

__

Triangle 1 – ∠1 = 50°, ∠2 = 30°

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

__

Triangle 1 – ∠1 = 60°, ∠2 = 20°

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

__

Triangle 1 – ∠1 = 25°, ∠2 = 115°

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

These triangles are similar.

__

Triangle 1 – ∠1 = 5°, ∠2 = 15°

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

These triangles are similar.

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