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Warm up

JM. BA. WC. OP. Warm up. No, corresponding sides are not congruent, and we can’t tell if the angles are congruent. No, the measures are not the same. Yes, angle measures are the same and the rays go to infinity.

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Warm up

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  1. JM BA WC OP Warm up No, corresponding sides are not congruent, and we can’t tell if the angles are congruent. No, the measures are not the same Yes, angle measures are the same and the rays go to infinity Yes, all corresponding sides are congruent and all corresponding angles are congruent. Yes, all corresponding parts are congruent. No, corresponding parts are not congruent. L  A  J  F  M  X  P  B  K  E  N  W  O  C

  2. 4.2 Shortcuts in Triangle Congruency Remember last time… We learned that two polygons were congruent if EACH corresponding pair of angles were congruent AND each pair of corresponding sides were congruent. Remember that you had to LIST EACH PAIR? Yikes! That could get very long and tedious (boring).

  3. Today… Today, you’re going to learn some shortcuts that apply to TRIANGLES ONLY. These shortcuts, if used correctly, will help you prove triangle congruency. Remember that congruency means EXACT size and shape… don’t confuse it with “similar”.

  4. AC PX AB PN CB XN Therefore, using SSS, ∆ABC= ∆PNX X A 3 inches 3 inches 5 inches 7 inches ~ P C B 7 inches N 5 inches ~ ~ ~ ~ = = = = Side Side Side If 2 triangles have 3 corresponding pairs of sides that are congruent, then the triangles are congruent.

  5. X CA XP CB XN C X Therefore, by SAS, ∆ABC ∆PNX 60° A 3 inches 5 inches 3 inches P N 60° C B 5 inches ~ ~ ~ ~ = = = = Side Angle Side If two sides and the INCLUDED ANGLE in one triangle are congruent to two sides and INCLUDED ANGLE in another triangle, then the triangles are congruent.

  6. CA XP A P C X Therefore, by ASA, ∆ABC ∆PNX ~ ~ ~ ~ = = = = Angle Side Angle If two angles and the INCLUDED SIDE of one triangle are congruent to two angles and the INCLUDED SIDE of another triangle, the two triangles are congruent. X 60° A 3 inches 3 inches 70° 70° P N 60° C B

  7. Remembering our shortcuts SSS ASA SAS (just so you know, there are 2 abbreviations that are not used for congruence: AAA and SSA)

  8. Let’s practice I need 3 volunteers to hand out white boards, markers and worksheets. The worksheet is called ‘page 828’… we’ll do section 4.2 together.

  9. Your Assignment Pg 220-222: 1-3, 8-19, 23-29

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