Answer:
1. ΔABC ~ ΔMPN by AA, similarity postulate
2. No two triangles among the triangles ΔRST, ΔKLM, and ΔJRW are similar
Step-by-step explanation:
1. It is required to show that two of the given triangles are similar;
ΔABC is a right triangle, [tex]\overline {AC}[/tex] = 8, [tex]\overline {CB}[/tex] = 12, ∠A = 38°
∴ ∠B = 90° - 38° = 52
The ratio of the legs = [tex]\overline {AC}[/tex]/[tex]\overline {CB}[/tex] = 8/12 = 2/3
ΔDEF is a right triangle, the legs [tex]\overline {DF}[/tex] = 10, and [tex]\overline {EF}[/tex] = 12
The ratio of the legs = [tex]\overline {DF}[/tex]/[tex]\overline {EF}[/tex] = 10/12 = 5/6
∴ ΔABC is not similar to ΔDEF as [tex]\overline {AC}[/tex]/[tex]\overline {CB}[/tex] ≠ [tex]\overline {DF}[/tex]/[tex]\overline {EF}[/tex]
ΔMPN is a right triangle, ∠M = 52°, therefore, ∠N = 90° - 52° = 38°
Two angles in triangle ΔMPN are equal to two angles in triangle ΔABC, therefore;
ΔABC ~ ΔMPN by Angle-Angle, AA, similarity postulate
2. The two given angles in ΔRST are ∠R = 45° and ∠S = 67°
The two given angles in ΔKLM are ∠K = 45° and ∠SL = 68°
The given angles in ΔJRW are ∠J = 21° and ∠R = 90° therefore, ∠W = 90 - 21 = 69°
No two triangles in ΔRST, ΔKLM, and ΔJRW are similar.
