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Which of the following theorems verifies that angle DEF ~ angle XZY?

Which of the following theorems verifies that angle DEF ~ angle XZY?-example-1
User Hamza Khursheed
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1 Answer

18 votes
18 votes

Step-by-step explanation: In this problem, notice that we're only given one pair of congruent angles, the 90 angles, but remember that the sum of the measures of the angles of a triangle is 180°.

So we can determine that the measure of the missing angle

of our first triangle is 40° because 90 + 50 + 40 = 180.

Now we have two pairs of congruent angles,

the 40° angles, and the 90° angles.

Therefore, since two of the angles of one triangle are congruent to

two of the angles of the other triangle, we can say that yes, the

triangles are similar by the Angle-Angle Similarity Postulate (AA~).

User Dario Corno
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