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In triangle FGH, FG = 12.3 cm, GH = 10.6 cm, Measure of angle G = 80 degrees, and Measure of angle H = 55 degrees. If Triangle A B C is congruent to triangle G H F, which statement is true? AB = 12.3 cm AB = 10.6 cm Measure of angle C = 55 degrees Measure of angle C = 80 degrees

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Question:

In triangle FGH, FG = 12.3 cm, GH = 10.6 cm, m angle G=80 degrees, and m angle H=55 degrees. If triangle ABC GHF, which statement is true?

(A) AB = 12.3 cm

(B) AB = 10.6 cm

(C) m∠C = 55°

(D) m∠C = 80°

Answer:

Option B:

AB = 10.6 cm

Solution:

The image of the triangle is attached below.

In ΔFGH,

FG = 12.3 cm, GH = 10.6 cm, m∠G = 80° and m∠H = 55°

Option A: AB = 12.3 cm

Given ΔGHF [tex]\sim[/tex] ΔABC.

Corresponding parts of congruence triangles are congruent.

GH = AB = 10.6 cm

So, option A is not true.

Option B: AB = 10.6 cm

Already proved in option A that AB = 10.6 cm

So, option B is true.

Option C: m∠C = 55°

ΔGHF [tex]\sim[/tex] ΔABC

Corresponding parts of congruence triangles are congruent.

m∠G = m∠A = 80°

m∠H = m∠B = 55°

Sum of the angles of a triangle = 180°

⇒ m∠A + m∠B + m∠C = 180°

⇒ 80° + 55° + m∠C = 180°

⇒ m∠C = 180° – 80° – 55°

⇒ m∠C = 45°

So, option C is not true.

Option D: m∠C = 80°

Already proved in option C that m∠C = 45°.

So, option D is not true.

Hence option B is the true statement that AB = 10.6 cm.

Ver imagen shilpa85475

Answer:

b

Step-by-step explanation:

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