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4.5 Even Answers 28. Not enough information given. 30. Not enough information given. 4.6 Isosceles Triangles and Right Triangles Goal 1: How to use properties of isosceles triangles to solve problems Goal 2: How to use properties of right triangles to solve problems in geometry In lesson 4.1, you learned that if an isosceles triangle has exactly two Congruent sides, then these sides are the legs of the triangle, and the Leg noncongruent side is the base. The two angles that have the base as one side are the base angles. Leg Base angles Base 4.6 Isosceles Triangles and Right Triangles Base Angles THM If two sides of a triangle are congruent , then the angles opposite them are congruent. N C Proof : Refer to the figure H Given : NC NY Prove : C Y Statements Y 1. Label H as the Reasons 1. Ruler Postulate midpoint of CY . 2. Draw NH 3. CH HY 4. NH NH 5. NC NY 6. NHC NHY 7. C Y 2. Two points determine a line. 3. Definition 4. Reflexive Prop. of 5. Given 6. SSS 7. CPCTC 4.6 Isosceles Triangles and Right Triangles If two angles of a triangle are congruent, then the sides opposite them are congruent. 4.6 Isosceles Triangles and Right Triangles If a triangle is equilateral, then it is also equiangular. 4.6 Isosceles Triangles and Right Triangles If a triangle is equiangular, then it is also equilateral. 34 2 1 An icosahedro n is a 3 - D figure that has 20 ' s as its faces. Each verte x of each is shared by 4 other ' s. An icosahedro n can be used to make a flat map used to approximat e distances on Earth' s surface. What % of Earth' s surface is occupied by North America? 34 2 1 An icosahedro n can be used to make a flat map used to approximat e distances on Earth' s surface. 4.6 Isosceles Triangles and Right Triangles HL Congruence THM If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of a 2nd right triangle, then the two triangles are congruent. The antena is to the plane containing the points B, C , D, and O. Each of the stays A running from the top of the antenna to B, C , and D uses the same length of cable. Is this enough informatio n to conclude AOB AOC AOD ? D B O C Yes By the HL THM 4.6 Isosceles Triangles and Right Triangles HW 4.6/11 - 19odd, 20 - 22, 25 - 33 odd 4.6 Even Answers 20. Since ABD CBD, AB BC , and ABE CBE by CPCTC ; BE BE by the Reflexive Prop. ABE CBE by SAS , and BAE BCE by CPCTC. 22. Since ABD CBD CDG CFG and all are equilateral; so ABD DBC DGC FGC by CPCTC and because an equilateral is equiangular. Then mABD mDBC mDGC mFGC by + Prop. of =. Then mABC mDGF by the + Post. and ABC DGF by definition.