1. Analyzing the two congruent triangles △LAP ≅ △GAT, we have:
a. T ⟷
b. G ⟷
c. AT ≅
d. LA ≅
e. ∠T ≅
f. ∠TAG ≅
g. ∠L ≅
h. △TAG ≅
2.
a.Answer:
☞ In the given conditions, LA measures 10 units. Since LA ≅ GA, GA also measures 10 units.
b.Answer:
☞In △LAP, ∠A measures 65° and ∠P measures 55°. Since, the sum of the interior angles of a triangle is 180°, 180-65-55=60.
c.Answer:
☞ In the given conditions, m∠P=55°. Since ∠P ≅ ∠T, ∠T also measures 55°.
d.Answer:
☞ In the given conditions, m∠LAP=65°. Since ∠LAP ≅ ∠GAT, ∠GAT also measures 65°.
e.Answer:
☞ To get the perimeter, we have to add the measures of all sides of △GAT.
☞ We are only given TA = 8 units so we will refer to the given measurements of the two other sides of △LAP since they are congruent. Thus, 8 units+ 10 units + 12 units = 30units.
Answers & Comments
Verified answer
1. Analyzing the two congruent triangles △LAP ≅ △GAT, we have:
2.
a. Answer:
☞ In the given conditions, LA measures 10 units. Since LA ≅ GA, GA also measures 10 units.
b. Answer:
☞ In △LAP, ∠A measures 65° and ∠P measures 55°. Since, the sum of the interior angles of a triangle is 180°, 180-65-55=60.
c. Answer:
☞ In the given conditions, m∠P=55°. Since ∠P ≅ ∠T, ∠T also measures 55°.
d. Answer:
☞ In the given conditions, m∠LAP=65°. Since ∠LAP ≅ ∠GAT, ∠GAT also measures 65°.
e. Answer:
☞ To get the perimeter, we have to add the measures of all sides of △GAT.
☞ We are only given TA = 8 units so we will refer to the given measurements of the two other sides of △LAP since they are congruent. Thus, 8 units+ 10 units + 12 units = 30 units.
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