Question

Show two of the triangles below are similar. Include a similarity statement and show work to support your statement. (The numbers on the first one that are blurry are 8’s)

Answer 1

1. ΔABC ~ ΔMPN by AA, similarity postulate

2. No two triangles among the triangles ΔRST, ΔKLM, and ΔJRW are similar

Explanation:

1. It is required to show that two of the given triangles are similar;

ΔABC is a right triangle,
`\overline {AC}` = 8,
`\overline {CB}` = 12, ∠A = 38°

∴ ∠B = 90° - 38° = 52

The ratio of the legs =
`\overline {AC}`/
`\overline {CB}` = 8/12 = 2/3

ΔDEF is a right triangle, the legs
`\overline {DF}` = 10, and
`\overline {EF}` = 12

The ratio of the legs =
`\overline {DF}`/
`\overline {EF}` = 10/12 = 5/6

∴ ΔABC is not similar to ΔDEF as
`\overline {AC}`/
`\overline {CB}` ≠
`\overline {DF}`/
`\overline {EF}`

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.