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Honors Geometry

Honors Geometry. Isosceles Triangles. Remember– the properties of an isosceles triangle…. Vertex Angle. Vertex Angle. Leg. Leg. Base Angles. Base. Investigating Isosceles Triangles.

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Honors Geometry

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  1. Honors Geometry Isosceles Triangles

  2. Remember– the properties of an isosceles triangle….. Vertex Angle Vertex Angle Leg Leg BaseAngles Base

  3. Investigating Isosceles Triangles • Use a straightedge to draw an ACUTE ISOSCELES triangle-- where and is the acute vertex angle. • Use scissors to cut the triangle out • Then fold the triangle as shown • REPEAT the procedure for an OBTUSE ISOSCELES triangle -- where and is the obtuse vertex angle. • What observation can you make about the base angles?

  4. Isosceles Triangle Theorem • If two sides of a triangle are congruent, then the angles opposite them are congruent.

  5. Use ALGEBRA to find the missing measures(not drawn to scale) • 1. 44 m r 30 x y

  6. Use ALGEBRA to find the missing measures(not drawn to scale) • 1. • x+y+ 44 = 180 Sum • x= y because the two base angles are congruent to each other b/c they are opposite congruent sides • 180 = x + x + 44 • 136 = 2x • 68=x • 68 = y 44 m r 30 68 68 x y

  7. Use ALGEBRA to find the missing measures(not drawn to scale) • 2. m r 30°

  8. Find the missing measures(not drawn to scale) • 30 + r + m = 180 • r is the other base angle and must be 30° b/c its opposite from a congruent side. • 30 + 30 + m = 180 • 60 + m = 180 • m = 120 • 2. m 120° r 30° 30°

  9. Isosceles Triangle Theorem • If two sides of a triangle are congruent, then the angles opposite them are congruent. • Given: • Prove:

  10. Proof of Base Angles Theorem • Statements • Label H as the midpoint of CY • Draw NH • Reasons • Ruler Postulate • 2 points determine a line • Def. of midpoint • Reflexive Prop • Given • SSS • CPCTC • Given: Prove:

  11. Converse of the Isosceles Triangle Theorem • If two angles of a triangle are congruent, then the sides opposite them are congruent. R A T

  12. Corollary-- • A corollary is a theorem that follows easily from a theorem that has already been prove. • Corollary : If triangle is equilateral, then it is also equiangular. A BC • Corollary : If a triangle is equiangular, then it is also equilateral. W • E R

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