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Bellwork – Write a theorem about the following Justify your theorem

"To accomplish great things, we must dream as well as act." Anatole France. Bellwork – Write a theorem about the following Justify your theorem. Leg-Leg Congruence Hypotenuse-Angle Congruence. Leg Angle Congruence Hypotenuse-Angle Congruence.

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Bellwork – Write a theorem about the following Justify your theorem

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  1. "To accomplish great things, we must dream as well as act." Anatole France Bellwork – Write a theorem about the followingJustify your theorem Leg-Leg Congruence Hypotenuse-Angle Congruence Leg Angle Congruence Hypotenuse-Angle Congruence

  2. "To accomplish great things, we must dream as well as act." Anatole France Bellwork – Write a theorem about the followingJustify your theorem Leg-Leg Congruence Hypotenuse- leg Congruence Leg Angle Congruence Hypotenuse-Angle Congruence If one leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent. If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle then the two triangles are congruent

  3. Chapter 4.6 Isosceles TrianglesObjective: To understand and be able to use the properties of isosceles and equilateral triangles. Check.4.10 Identify and apply properties and relationships of special figures (e.g., isosceles and equilateral triangles, family of quadrilaterals, polygons, and solids). Spi.4.3 Identify, describe and/or apply the relationships and theorems involving different types of triangles, quadrilaterals and other polygons.

  4. What are the 5 ways to prove Triangles congruent a. SSS, Side SideSide b. SAS, Side Angle Side c. ASA, Angle Side Angle d. AAS, Angle Angle Side e. SSSAAA 3 sides, 3 angles f. What does CPCTC mean?

  5. R S P Given: PQR, PQRQ Prove: P  R Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent. If AB CB then A  C If two angles of a triangle are congruent, then the sides opposite those angles are congruent. If A  C then AB CB B B Q Statement • Let S be midpoint of PR • Draw a segment SQ • PS RS • QS QS • PQRQ • PQS RQS • P  R Reason • Every segment has one midpoint • Two points determine a line • Midpoint Theorem • Reflexive Property • Given • SSS • CPCTC C C A A Check.4.10 Identify and apply properties and relationships of special figures (e.g., isosceles and equilateral triangles, family of quadrilaterals, polygons, and solids).

  6. What about an equilateral triangle? Each Angle of an Equilateral Triangle = 60 A = 60 B = 60 C = 60 • If ABBCCA • ABBC then A  C • BCCA then A  B • What does A, B and C equal? • A +B + C = 180 • 3 A = 180 • A = 60, • B = 60, C = 60 B B C C A A

  7. K Find the missing measure G J H If GHHK, HJJK and mGJK = 100 What is the measure of HGK? KHJ + HKJ + KJH = 180 KHJ = HKJ, set equal to x x+ x + 100 = 180 2x = 180-100= 80 x = 40 KHJ = HKJ, = 40 KHG + KHJ = 180 KHG = 140 KHG + HGK + GKH = 180 HGK = GKH, set to y 140 + 2y = 180 2y = 40 y = 20 HGK = GKH = 20

  8. Find the missing measure EFG is equilateral and EH bisects E Find m1 and m2 E m1 + m2 = 60 m1 = m 2 – bisector m1 = 60/2 = 30 EFH + m1 + EHF = 180 60+ 30 + 15x = 180 15x = 90 x = 6 2 1 15x F G H

  9. Find the missing measure EFG is equilateral and EH bisects E, EJ bisects 2 Find HEJ and EJH and EJG m1 + m2 = 60 m1 = m 2 – bisector m1 = 60/2 = 30 EFH + m1 + EHF = 180 60+ 30 + 15x = 180 15x = 90 x = 6 E 2 1 HEJ = 1/2 m 2 – bisector HEJ = ½ (30) =15 HEJ + EJH + JHE = 180 15 + EJH + 90= 180 EJH = 75 EJG = 105 15x F G J H

  10. Practice Assignment • Page 287, 10 – 24 even • Honors; page 288 16 – 42 even

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