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 up and equal ______. 180 

Exterior Angle Theorem The 2 remote interior angles add up and equal the exterior angle Exterior Angle Remote 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.

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.

Find the center of dilation

Similar Polygons 1.Corresponding angles are congruent 2.Corresponding sides are proportional 3.Similarity Statement

Solve for x and y. x = 26 cm A B C S L T x 5 cm y = 12 cm 24 cm 10 cm 13 cm y

In similar triangles, angles are congruent and sides are proportional A B C S L T Find the missing angle measures.

12 cm4 cm Perimeter = 60 cm Perimeter = x x = 20 cm Find the perimeter of the smaller triangle.

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. 43° 68° W V U 7 11 X Y Z 5 3

Prove that  RST ~  PSQ R S T P Q Two sides are proportional 2. Included angle is congruent SAS~

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?

Trig Ratios

Trig Ratio What is cos R? What is sin R? What is tan R?

Co-Function Relationships

Cos 64  = Sin ____ 26 

Find a Missing Side x = 17.6 x Solve for x. Round to the nearest tenth.

Find a Missing Angle  = 31.4  Solve for . Round to the nearest tenth. 

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