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 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 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.
