Chapter 7.1 Common Core G.SRT.5 - Use…similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Objective – To write ratios and solve proportions.

Chapter 7.1 Notes Ratio – if a and b are 2 quantities that are measured in the same units, then the ratio of a to b is a/b. (i.e. a ratio is a fraction) Proportion – is an equation that equates 2 ratios Means a = c Extremes b d

Properties of Proportions If a = c, then ad = bc (Cross Product Prop.) b d If a = c, then b = d (Reciprocal Prop.) b d a c

Properties of Proportions If a = c, then a = b (Rotation) b d c d If a = c, then a+ b = c + d b d b d (Add the denominator to the numerator)

Chapter 7.2 Common Core G.SRT.5 - Use…similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Objective – To identify and apply similar polygons.

Chapter 7.2 Notes Similar Polygons – when you have 2 polygons that have all corresponding ∠’s are ≌ and all corresponding sides are in the same proportion then they are similar (~) A X Y Z B C

Thm – if 2 polygons are ~, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths Scale Factor – if 2 polygons are ~, then the ratio of the lengths of 2 corresponding side is called the scale factor. We usually write scale factors like this a:b

Chapter 7.3 Common Core G.SRT.5 & G.GPE.5 – Use…similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems. Objectives – To use the AA Postulate, SAS, & SSS similarity Theorems. To use similarity to find indirect measurements.

Chapter 7.3 Notes Similar Triangles 1) AA (angle-angle similarity postulate) If 2 ∠’s of one triangle are ≌ to 2 ∠’s of another triangle, then the 2 ∠’s are ~

Similar Triangles 2) SSS (side-side-side similarity postulate) 3) SAS (side-angle-side similarity postulate)

Chapter 7.4 Common Core G.SRT.5 & G.GPE.5 – Use…similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems. Objective – To find and use relationships in similar right triangles.

Chapter 7.4 Notes Thm – if the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. 1 ~ 2 ~ the big 1 2

Parachute Bob (Geometric Mean Thm)

Chapter 7.5 Common Core G.SRT.4 – Prove theorems about triangles…a line parallel to one side of a triangle divides the other two proportionally. Objective – To use the Side-Splitter Theorem and the Triangle-Angle-Bisector Theorem.

Chapter 7.5 Notes Side Splitter Thm Ifthen

Thm Ifthen Thm Ifthen