Transcript SAS
CCGPS Analytic Geometry GEOMETRY!!! 5 Ways to Prove Triangles Congruent 1. SSS: All 3 sides are exactly the same 2. SAS: 2 congruent sides and the angle in between 3. ASA: 2 congruent angles are the side in between 4. AAS: 2 congruent angles and a side NOT in between 5. HL: ONLY FOR RIGHT TRIANGLES – Hypotenuse and 1 Leg CONGRUENCE STATEMENT Order matters! Match up corresponding parts. Example: ABC DEF Triangle Sum The 3 angles in a triangle add 180 up and equal ______. Exterior Angle Theorem The 2 remote interior angles add up and equal the exterior angle Remote Angle Exterior Angle Remote Angle Isosceles Triangle • 2 congruent sides • Opposite of the congruent sides are congruent angles Rigid Motion – the shape will still be congruent after the move 1. Reflection 2. Translation 3. Rotation Dilate the figure by 1/2. Use the origin as the center of dilation. A 4,4 A ' 2,2 B 2, 6 B ' 1, 3 C 6,0 C ' 3,0 Dilate the figure by 2. Use (-2,0) as the origin as the center of dilation. To do this, you have to calculate the distance each point is away from the center of dilation and then multiply that distance by the dilation factor. A 0,0 A ' 2,0 B 0,3 C 2,3 D 2,0 B ' 2,6 C ' 6,6 D ' 6,0 Find the center of dilation Center 2,2 Similar Polygons 1. Corresponding angles are congruent 2. Corresponding sides are proportional 3. Similarity Statement ABC ~ DEF Solve for x and y. ABC ~ SLT L A 10 cm B x 24 cm x = 26 cm y 5 cm S 13 cm C T y = 12 cm In similar triangles, angles are congruent and sides are proportional ABC ~ SLT Find the missing angle measures. A L 53 S B C 37 T mC 37 mL 90 mS 53 Find the perimeter of the smaller triangle. 12 cm Perimeter = 60 cm 4 cm Perimeter = x x = 20 cm 3 ways to Prove Triangles Similar 1)Angle-Angle (AA~) Similarity Postulate 2)Side-Side-Side (SSS~) Similarity Theroem 3)Side-Angle-Side (SAS~) Similarity Thm Determine whether the triangles are similar. If so, tell which similarity test is used and complete the statement. 68° 43° 68° 43° V Y 7 W 11 3 U X 5 Z Prove that RST ~ PSQ 1. Two sides are proportional SAS~2. Included angle is congruent S 4 P 12 R 5 16 20 4 5 4 4 1 1 Q 15 T S S reflexive A tree cast a shadow 18 feet long. At the same time a person who is 6 feet tall cast a shadow 4 feet long. How tall is the tree? tree's shadow tree's height person's shadow person's height 18 x 4 6 x 27 Trig Ratios Trig Ratio What is cos R? What is sin R? What is tan R? 21 29 20 29 20 21 Co-Function Relationships sin cos(90 ) cos sin(90 ) 1 tan tan(90 ) Co-Function Relationships 26 Cos 64 = Sin ____ Find a Missing Side Solve for x. Round to the nearest tenth. x = 17.6 x Find a Missing Angle Solve for . Round to the nearest tenth. = 31.4 The angle of elevation from a ship to the top of a 35 meter lighthouse on the coast measures 26. How far from the coast is the ship? Round to the nearest tenth. tan 26 = 35/x x = 71.8 m