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Warm Up

Warm Up. Write a congruence statement List all corresponding sides and angles using the following congruence statement. Agenda. Warm Up Homework Check 4-2, 4-3, 4-6 Triangle Congruence Figures Homework. Practice 4-1 Homework Check:. 1. <1 = 110, <2=120 2. <4=135, <3=90

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Warm Up

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  1. Warm Up • Write a congruence statement • List all corresponding sides and angles using the following congruence statement

  2. Agenda • Warm Up • Homework Check • 4-2, 4-3, 4-6 Triangle Congruence Figures • Homework

  3. Practice 4-1 Homework Check: 1. <1 = 110, <2=120 2. <4=135, <3=90 3. <5=140, <6=90, <7=40, <8 = 90 4. 5. 6. 7. • FCB 2. NMD 3. GTK 4. 5. 6. 7. <Q 8. RS 9. <QRS 10. SQ 11. QR 12. <QSR

  4. Today’s Objective • Use triangle congruence postulates and theorems to prove that triangles are congruent.

  5. 4-2, 4-3, 4-6 Triangle Congruence Figures Review Last week we found out that if two triangles have three congruent sides and three congruent angles then the two triangles must be ____________ Just like with similarity, we don’t need all six of these to prove triangles are congruent.

  6. If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

  7. If two sides and the included(between) angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

  8. Non-example of SAS: • Why can’t we use SAS to show these triangles are congruent?

  9. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

  10. If two angles and a non-includedside of one triangle are congruent to two angles and the correspondingnon-included side of another triangle, then the triangles are congruent.

  11. Special Theorem for Right Triangles: ***Only true for Right Triangles*** Remember: Hypotenuse: Longest side, always opposite the right angle. Legs: Other 2 shorter sides (form the right angle)

  12. Hypotenuse – Leg (HL) Theorem If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.

  13. We now have the following: • SSS – side, side, side • SAS – Side, Angle (between), Side • ASA – Angle, Side (between), Angle • AAS/SAA – Angle, Angle, Side (Not between) • HL – Hypotenuse, Leg

  14. NEVER USE THESE!!!!!! Or the Reverse (NEVER write a curse word on your paper!!!)

  15. Examples Which Theorem proves the Triangles are congruent? 1.

  16. 2.

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  19. 5.

  20. Class Work Complete the work sheet for classwork!

  21. Homework Finish worksheet

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