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Aim 3.2: How can we prove Triangles to be congruent?

Aim 3.2: How can we prove Triangles to be congruent?. Do Now: 1. Write the 4 methods which a triangle can be congruent 2. How is the following triangle congruent? Homework: Page 3 #1 - 2. Aim 3.2: How can we prove Triangles to be congruent?. Example:. Given: AB is parallel to EF

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Aim 3.2: How can we prove Triangles to be congruent?

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  1. Aim 3.2: How can we prove Triangles to be congruent? Do Now: 1. Write the 4 methods which a triangle can be congruent 2. How is the following triangle congruent? Homework: Page 3 #1 - 2

  2. Aim 3.2: How can we prove Triangles to be congruent? Example: Given: AB is parallel to EF Angle A Angle F AB EF Prove: ABC DEF A D E B C F

  3. Aim 3.2: How can we prove Triangles to be congruent? Midpoint 1. Given 1. B is the midpoint of AC • A midpoint cuts a line segment into two congruent parts. 2. Mdpt cuts a line in ½ 2. AB BC A B C

  4. Aim 3.2: How can we prove Triangles to be congruent? Median CD is a median to AB 1. Given D is the mdpt of AB 2. Median hits the base at the mdpt AD BD 3. Mdpt of a line segment cuts a line segment in ½ C A B D

  5. Aim 3.2: How can we prove Triangles to be congruent? Perpendicular D BD is perpendicular to AC 1. Given Angles 1 & 2 are right 2. Perpendicular angles lines form right angles 3. Angle 1 Angle 2 3. All right angles are 1 2 A B C

  6. Aim 3.2: How can we prove Triangles to be congruent? Altitude CD is an altitude to AB 1. Given CD AB 2. Altitude is to the base 1 & 2 are right angles 3. lines form right 1 2 4. All right are C A D B

  7. Aim 3.2: How can we prove Triangles to be congruent? Example: Given: AD is perpendicular to CB AD bisects BC Prove: Triangle ADB Triangle ADC A C D B

  8. Aim 3.2: How can we prove Triangles to be congruent? Isosceles Triangle: Sides are given A B C AB AC 1. Given Triangle ABC is isosceles 2. When 2 sides are =, the triangle is Isosceles Angle B Angle C 3. Isosceles triangles have base angles

  9. Aim 3.2: How can we prove Triangles to be congruent? Isosceles Triangle: Angles are given A B C Angle B Angle C 1. Given Triangle ABC is Isosceles 2. When 2 base angles are , the triangle is Isosceles AB AC 3. Sides opposite the base angles are

  10. Aim 3.2: How can we prove Triangles to be congruent? Supplementary 1 2 3 4 1. Angle 2 Angle 3 1. Given 2. Angle 1 Angle 4 2. Supplements of congruent angles are congruent

  11. Aim 3.2: How can we prove Triangles to be congruent? Example: Packet Page 5 #9 D A X C B Given: X is the midpoint of BD X is the midpoint of AC Prove: DXC BXA

  12. Aim 3.2: How can we prove Triangles to be congruent? Example: Packet Page 5 #11 B A C D E Given: AD bisects BE AB DE Prove: ABC DEC

  13. Aim 3.2: How can we prove Triangles to be congruent? Example: Packet Page 5 #12 H J B L Given: Angle J Angle L B is the midpoint of JL Prove: JHB LCB C

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