Question

3 - 9 practice online
geometry (81 p01 rm h218) sharp, jeffrey / unit 3 - similarity / lesson 3 - 9 conditions for triangle simila

1. in triangle abc, angle a is 35° and angle b is 20°.

select all triangles which are similar to triangle abc.
triangle ghi where angle g is 35° and angle i is 30°
triangle mno where angle n is 20° and angle o is 125°
triangle def where angle d is 35° and angle e is 20°
triangle jkl where angle j is 35° and angle l is 125°
triangle pqr where angle q is 20° and angle r is 30°

Explanation:

Step1: Calculate the third angle of triangle \(ABC\)

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle of \(\triangle ABC\) be \(C\). Then \(C = 180^{\circ}-(35^{\circ}+ 20^{\circ})=125^{\circ}\)

Step2: Check each triangle

• For \(\triangle GHI\):

Sum of given angles \(35^{\circ}+30^{\circ}=65^{\circ}
eq180^{\circ}\) (after calculating the third angle \(180 - 65=115^{\circ}\)), not similar.

• For \(\triangle MNO\):

Third angle \(M=180-(20 + 125)=35^{\circ}\). Angles \(20^{\circ},35^{\circ},125^{\circ}\), similar.

• For \(\triangle DEF\):

Third angle \(F=180-(35 + 20)=125^{\circ}\). Angles \(20^{\circ},35^{\circ},125^{\circ}\), similar.

• For \(\triangle JKL\):

Third angle \(K=180-(35 + 125)=20^{\circ}\). Angles \(20^{\circ},35^{\circ},125^{\circ}\), similar.

• For \(\triangle PQR\):

Sum of given angles \(20^{\circ}+30^{\circ}=50^{\circ}
eq180^{\circ}\) (after calculating the third angle \(180 - 50 = 130^{\circ}\)), not similar.

Answer:

B. triangle \(MNO\) where angle \(N\) is \(20^{\circ}\) and angle \(O\) is \(125^{\circ}\)
C. triangle \(DEF\) where angle \(D\) is \(35^{\circ}\) and angle \(E\) is \(20^{\circ}\)
D. triangle \(JKL\) where angle \(J\) is \(35^{\circ}\) and angle \(L\) is \(125^{\circ}\)