Question

in triangle abc, angle a is 35° and angle b is 20°. determine whether each triangle is similar to triangle abc.

	similar	not similar
b. triangle ghi, where angle g is 35° and angle i is 30°.	○	○
c. triangle jkl, where angle j is 20° and angle l is 30°.	○	○
d. triangle mno, where angle n is 20° and angle o is 125°.	○	○
e. triangle pqr, where angle p is 35° and angle r is 125°.	○	○

Explanation:

First, find the third angle of triangle \( ABC \). The sum of angles in a triangle is \( 180^\circ \). So angle \( C = 180^\circ - 35^\circ - 20^\circ = 125^\circ \). Two triangles are similar if their corresponding angles are equal (AA similarity criterion).

Step 1: Analyze Triangle DEF

Angle \( D = 35^\circ \), angle \( E = 20^\circ \). Third angle \( F = 180 - 35 - 20 = 125^\circ \). Angles match \( ABC \) (35°, 20°, 125°), so similar.

Step 2: Analyze Triangle GHI

Angle \( G = 35^\circ \), angle \( I = 30^\circ \). Third angle \( H = 180 - 35 - 30 = 115^\circ \). Angles don't match \( ABC \), so not similar.

Step 3: Analyze Triangle JKL

Angle \( J = 20^\circ \), angle \( L = 30^\circ \). Third angle \( K = 180 - 20 - 30 = 130^\circ \). Angles don't match \( ABC \), so not similar.

Step 4: Analyze Triangle MNO

Angle \( N = 20^\circ \), angle \( O = 125^\circ \). Third angle \( M = 180 - 20 - 125 = 35^\circ \). Angles match \( ABC \) (35°, 20°, 125°), so similar.

Step 5: Analyze Triangle PQR

Angle \( P = 35^\circ \), angle \( R = 125^\circ \). Third angle \( Q = 180 - 35 - 125 = 20^\circ \). Angles match \( ABC \) (35°, 20°, 125°), so similar.

Answer:

• A. Triangle DEF: SIMILAR (angles 35°, 20°, 125° match ABC)
• B. Triangle GHI: NOT SIMILAR (angles 35°, 30°, 115° don't match)
• C. Triangle JKL: NOT SIMILAR (angles 20°, 30°, 130° don't match)
• D. Triangle MNO: SIMILAR (angles 35°, 20°, 125° match ABC)
• E. Triangle PQR: SIMILAR (angles 35°, 20°, 125° match ABC)

So marking:
A: SIMILAR
B: NOT SIMILAR
C: NOT SIMILAR
D: SIMILAR
E: SIMILAR