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

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


[tex]Which of the following theorems verifies that angle DEF ~ angle XZY?[/tex]

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  1. 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~).

  2. 56.6

    step-by-step explanation:

    the ratio of the perimeters is equal to the scale.

    the ratio of the areas is equal to the square of the scale.

    34 / 20 = k

    a / 19.6 = k²

    substituting:

    a / 19.6 = (34 / 20)²

    a = 19.6 (34 / 20)²

    a ≈ 56.6

    [tex]These figures are similar. the perimeter and area of one are given. the perimeter of the other is al[/tex]

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