# ANGLE ANGLE SIMILARITY WORKSHEET

In each case, explain whether two triangles are similar using Angle-Angle Similarity Theorem.

Problem 1 :

Problem 2 :

Problem 3 :

The figure shows only one pair of congruent angles. Find the measure of the third angle in each triangle.

Triangle PQR :

Write the Triangle Sum Theorem for this triangle.

m∠P + m∠Q + m∠R  =  180°

Substitute the given angle measures.

45° + 100° + m∠R  =  180°

Simplify.

145° + m∠R  =  180°

Subtract 145° from both sides.

145° + m∠R - 145°  =  180° - 145°

Simplify.

m∠R  =  35°

Triangle STU :

Write the Triangle Sum Theorem for this triangle.

m∠S + m∠T + m∠U  =  180°

Substitute the given angle measures.

m∠S + 100° + 35°  =  180°

Simplify.

m∠S + 135°  =  180°

Subtract 135° from both sides.

m∠S + 135° - 135°  =  180° - 135°

Simplify.

m∠S  =  45°

Conclusion :

Three Angles of triangle PQR are 45°, 100° and 35°.

Three Angles of triangle STU are 45°, 100° and 35°.

Because two angles in one triangle are congruent to two angles in the other triangle, the two triangles are similar.

The figure shows only one pair of congruent angles. Find the measure of the third angle in each triangle.

Triangle ABC :

Write the Triangle Sum Theorem for this triangle.

m∠A + m∠B + m∠C  =  180°

Substitute the given angle measures.

m∠A + 58° + 70°  =  180°

Simplify.

m∠A + 128°  =  180°

Subtract 128° from both sides.

m∠A + 128° - 128°  =  180° - 128°

Simplify.

m∠A  =  52°

Triangle DEF :

Write the Triangle Sum Theorem for this triangle.

m∠D + m∠E + m∠F  =  180°

Substitute the given angle measures.

70° + m∠E + 49°  =  180°

Simplify.

m∠E + 119°  =  180°

Subtract 119° from both sides.

m∠E + 119° - 119°  =  180° - 119°

Simplify.

m∠E  =  61°

Conclusion :

Three Angles of triangle ABC are 52°, 58° and 70°.

Three Angles of triangle DEF are 70°, 61° and 49°.

Because only one angle is congruent, the two triangles are not similar.

The figure shows only one pair of congruent angles. Find the measure of the third angle in each triangle.

Triangle ABC :

Write the Triangle Sum Theorem for this triangle.

m∠A + m∠B + m∠C  =  180°

Substitute the given angle measures.

41° + m∠B + 30°  =  180°

Simplify.

m∠B + 71°  =  180°

Subtract 71° from both sides.

m∠B + 71° - 71°  =  180° - 71°

Simplify.

m∠B  =  109°

Triangle DEF :

Write the Triangle Sum Theorem for this triangle.

m∠D + m∠E + m∠F  =  180°

Substitute the given angle measures.

m∠D + 109° + 30°  =  180°

Simplify.

m∠D + 139°  =  180°

Subtract 130° from both sides.

m∠D + 139° - 139°  =  180° - 139°

Simplify.

m∠D  =  41°

Conclusion :

Three Angles of triangle ABC are 41°, 109° and 30°.

Three Angles of triangle DEF are 41°, 109° and 30°.

Because two angles in one triangle are congruent to two angles in the other triangle, the two triangles are similar.

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