SIMILAR TRIANGLES SIMILAR TRIANGLES have the same shape, but not necessarily the same size.

SIMILAR TRIANGLES TEST FOR SIMILARITY #1 If the angles of one triangle are equal to the corresponding angles of the other triangle, the triangles are SIMILAR. 60° 70° 50°

SIMILAR TRIANGLES TEST FOR SIMILARITY #2 If the lengths of the sides of one triangle form equal ratios to the corresponding sides of the other triangle, the triangles are SIMILAR. 12 cm 6 cm 16 cm 8 cm 9 cm 18 cm

SIMILAR TRIANGLES Find the missing measures of this pair of similar triangles. y z 48° 72° 60° x x = y = z = 60° 12(3) = 36 7(3) = 21 A B C Y X Z

SIMILAR TRIANGLES Find the missing measures. y x 25° w u = 65° A B C D E z u The sum of the angles of a triangle is 180°. So, m ACB (u) = 180 – 25 – 90 65°

SIMILAR TRIANGLES Find the missing measures. y x 25° w u = 65° A B C D E z u w = 65° m ACB (u) = m AED (w). 65°

SIMILAR TRIANGLES Find the missing measures. y x 25° w u = 65° A B C D E z u w = x = 65° To find x, use Pythagorean’s Theorem x 2 = 22 2 – 9 2 = 403

SIMILAR TRIANGLES Find the missing measures x 25° w u = 65° A B C D E u w = x = 65° To find y, find the ratio of sides AE ÷ AC = 28 ÷ 22 = y = So, y = (9)(1.2727) y z

SIMILAR TRIANGLES Find the missing measures x 25° w u = 65° A B C D E u w = x = 65° To find z, use the ratio of sides AD = y = So, z = – z = = (20.075)(1.2727) y z

TRIGONOMETRIC RATIOS A B C OPP. ADJ. HYP.

TRIGONOMETRIC RATIOS A B C OPP. ADJ.HYP.

TRIGONOMETRIC RATIOS A B C 20 ft 8 ft. Find the measure of angle C.

TRIGONOMETRIC RATIOS A B C 32° 8 ft. Find the length of AC. x

TRIGONOMETRIC RATIOS A B C 75° 58 m Find the length of AB. x

TRIGONOMETRIC RATIOS A B C REVIEW