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HOME-ROOM

Learn to prove congruent triangles using SSS, SAS postulates. Understand two-column proofs & guided practice. Get ready for HW assignments.

dwieczorek
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HOME-ROOM

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  1. HOME-ROOM

  2. BELL-WORK Complete the two-column proof below of TB pg 256 Guided Practice 4 Statements Reasons 1. Angle J is congruent to angle P Segment JK is congruent to segment PM Segment JL is congruent to segment PL L bisects segment KM 2. Angle JLK is congruent to angle PLM 3. Segment LK is congruent to segment LM 4. Angle K is congruent to angle M 5. Triangle JLK is congruent to triangle PLM

  3. HW 2.1(c) Due 10/19/18: PW 4-4 # 1,2,4-7

  4. HW 2.1(b) Solutions • Triangle ABC is congruent to triangle DRS. • Triangle LMN is congruent to triangle QPN. • 48 • 5

  5. Guiding question: What are the SSS and SAS postulates?

  6. Congruent Triangles If two triangles have three pairs of congruent corresponding angles and three pairs of congruent corresponding sides, then.. the triangles are congruent. We do not need to know that all six corresponding parts are congruent in order to conclude that two triangles are congruent. Yesterday we learned that if two angles of one triangle are congruent to two angles of another triangle, by the… third angles theorem, the third angles are congruent. Today we will learn how to prove that triangles are congruent.

  7. Congruent Triangles It is enough to know only that corresponding sides are congruent. Side-Side-Side (SSS) Postulate: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

  8. Congruent Triangles Side-Side-Side (SSS) Postulate: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

  9. Congruent Triangles Side-Side-Side (SSS) Postulate: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

  10. Congruent Triangles Given that M is the midpoint of segment XY, and segment AX is congruent to segment AY, write a paragraph proof to prove ΔAMX is congruent to ΔAMY.

  11. Congruent Triangles TB pg 262 Guided Practice 1

  12. Congruent Triangles Without graphing, prove whether the triangle with vertices J(2,5), K(1,1) and L(5,2) is congruent to the triangle with vertices N(-3,0), P(-7,1) and Q(-4,4). JL = √18 QP = √18 LK = √17 PN = √17 KJ = √17 NQ = √17 Therefore ∆JKL ~ ∆QNP by SSS.

  13. Congruent Triangles I estimate the width of a heavy box, with my hands, to help decide whether the box will fit through the door way. A triangle is made between by head and the box. (pg 187) If I keep my hands the same, when I line up with the door way, the triangle formed without the box is congruent to the one with the box because: (a) The 2 lengths of my arms are the same The angle formed between by arms is the same This indicates… if 2 lengths and the included angle of 2 triangles are congruent, then the triangles are congruent.

  14. Congruent Triangles Side-Angle-Side (SAS) Postulate: If the two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

  15. Congruent Triangles Side-Angle-Side (SAS) Postulate: If the two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

  16. Congruent Triangles Side-Angle-Side (SAS) Postulate: If the two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

  17. Congruent Triangles Given that segment AD is congruent to segment BC, what other information do you need to prove ΔADC is congruent to ΔBCD?

  18. Congruent Triangles TB pg 265 Guided Practice 3 Statements Reasons 1. Segment FG is congruent to segment GH Segment JG bisects angle FGH 2. Angle FGJ is congruent to angle HGJ Segment GJ is congruent to segment GJ Triangle FGJ is congruent to triangle HGJ

  19. Congruent Triangles Given that angle RSG is congruent to angle RSH, and segment SG is congruent to segment SH, can you prove that triangle RSG is congruent to triangle RSH?

  20. Congruent Triangles TB pg 266 Guided Practice 4 Statements Reasons 1. Segment MN is congruent to segment PN Segment LM is congruent to segment LP 2. Segment LN is congruent to segment LN Triangle LNM is congruent to triangle LNP Angle LNM is congruent to angle LNP

  21. Who wants to answer the Guiding question? What are the SSS and SAS postulates?

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