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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 and<A <J and<F <M and<X <P and<B <K and<E < N and<W <O and<C

  2. 4.2 Shortcuts in Triangle Congruency What postulate is that? Last time, we learned: IF two polygons were congruent THEN each corresponding pair of angles were congruent AND each pair of corresponding sides were congruent. Remember, in a proof, we had to LIST EACH PAIR? Polygon Congruence Postulate

  3. You are given this graphic and statement. Write a 2 column proof. Like this: X ~ Prove: ΔLXM = ΔYXM Statements Reasons XY = XL LM = YM XM = XM <L = <Y <XMY = < XML <LXM = < YXM ΔLXM = ΔYXM ~ Given ~ Given ~ Reflexive Property ~ Given L Y ~ M All right angles are congruent ~ Third Angle Theorem Polygon Congruence Postulate ~

  4. 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”.

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

  6. X CA XP CB XN <C <X ∆ABC ∆PNX A P N C B ~ = ~ ~ ~ = = = Side Angle Side Iftwo sides and the INCLUDED ANGLE in one triangle are congruent to two sides and INCLUDED ANGLE in another triangle, then the triangles are congruent. Statements Reasons Angles are INCLUDED between the congruent sides Given Given Given SAS Congruency Statement

  7. Angle Side Angle CA XP <A <P <C <X Therefore, by ASA, ∆ABC = ∆PNX ~ ~ ~ ~ = = = 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 See how the side is INCLUDED between the two angles. A P N Congruency Statement C B

  8. There are two kinds of shortcuts Ones that work SSS SAS ASA AAS HL (right triangles only) Ones that don’t AAA SSA

  9. Let’s practice What other information, if any, do you need to prove the two triangles congruent by SAS? Explain. To start, list the pairs of congruent, corresponding parts you already know. <Y <S ~ ~ What else? <B = <G <Z = <T What else? HG GF YZ ST XZ RT

  10. Get the following: • 3 pieces of patty paper • Ruler with centimeters • Your compass • pencil We are going to do 3 constructions… You have to, have to, have to, following these directions exactly. If you have a question or get stuck, please be sure to get help ♥♥

  11. 1st Construction On one piece of patty paper, off to the side, create 3 line segments: mBC = 4cm, mAC = 6 cm and, mAB = 8 cm Construction of a triangle given three side lengths. • Duplicate AB • Measure AC, duplicate it at A • Measure BC, duplicate it at B • The point of intersection is C • Connect the points to create ∆ABC

  12. 2nd Construction On one piece of patty paper, off to the side, create 2 line segments and an angle: mAC = 6 cm, mAB = 8 cm, m<A = 30◦ • Duplicate <A • Duplicate AB on one ray • Duplicate AC on the other • Connect BC Construction of a triangle given 2 side lengths and an included angle.

  13. 3rd Construction On one piece of patty paper, off to the side, create 1 line segment and 2 angles: mAB = 7 cm, m<A = 35◦, m<B = 50 ◦ • Duplicate AB • At vertex A, duplicate <A • At vertex B, duplicate <B • Name the point where the rays of the angles intersect, C. Construction of a triangle given 2 angles and an included side.

  14. Your Assignment Go to mathplease.com Click through to facebook Add a comment under today’s discussion

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