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QuestionIf △AFG∼△RHT\triangle \mathrm{AFG} \sim \triangle \mathrm{RHT}, find ∠A≅\angle A \cong which corresponds to which angle? a. ∠R\angle \mathrm{R} b. ∠H\angle \mathrm{H} c. ∠T\angle T d. ∠G\angle G

Studdy Solution

STEP 1

Assumptions1. △AFG\triangle AFG is similar to △RHT\triangle RHT. . In similar triangles, corresponding angles are congruent.

STEP 2

We know that in similar triangles, the corresponding angles are congruent. This means that the angle at the same relative position in each triangle is equal.

STEP 3

Let's identify the corresponding angles in the two triangles.In △AFG\triangle AFG, the angles are AA, $$, and $G$.
In △RHT\triangle RHT, the angles are RR, HH, and $$.
By the definition of similar triangles, ∠A\angle A corresponds to ∠R\angle R, ∠F\angle F corresponds to ∠H\angle H, and ∠G\angle G corresponds to ∠\angle.

STEP 4

Now, we can answer the questions.
a. ∠A≅∠R\angle A \cong \angle R because they are corresponding angles in similar triangles.
b. ∠A\angle A is not congruent to ∠H\angle H because they are not corresponding angles.
c. ∠A\angle A is not congruent to ∠\angle because they are not corresponding angles.
d. ∠A\angle A is not congruent to ∠G\angle G because they are not corresponding angles.

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