CONGRUENT TRIANGLES.

Slides:



Advertisements
Similar presentations
4-5 Warm Up Lesson Presentation Lesson Quiz
Advertisements

4-7 Section 4.7 Triangle Congruence: ASA, AAS, and HL Holt Geometry
4-6 Warm Up Lesson Presentation Lesson Quiz
4-5 Warm Up Lesson Presentation Lesson Quiz
8. BC = ED = 4; BC = EC = 3; DC = DC by Reflex so Δ BCD  ΔEDC by SSS 9. KJ = LJ; GK = GL; GJ = GJ by Reflex so ΔGJK  ΔGJL by SSS 12. YZ = 24, ST = 20,
Objective SWBAT prove triangles congruent by using ASA and AAS.
4-6 Warm Up Lesson Presentation Lesson Quiz
Triangle Congruence: SSS and SAS
1 Objectives Define congruent polygons Prove that two triangles are congruent using SSS, SAS, ASA, and AAS shortcuts.
Warm Up 1. Name the angle formed by AB and AC. 2.Name the three sides of ABC. 3. ∆ QRS  ∆ LMN. Name all pairs of congruent corresponding parts. Possible.
Warm Up Lesson Presentation Lesson Quiz.
Learning Targets I will apply the ASA Postulate, the AAS Theorem, and the HL Theorem to construct triangles and to solve problems. I will prove triangles.
Do Now 1. ∆ QRS  ∆ LMN. Name all pairs of congruent corresponding parts. 2.Find the equation of the line through the points (3, 7) and (5, 1) QR  LM,
Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL 4-5 Triangle Congruence: ASA, AAS, and HL Holt Geometry Warm Up Warm Up Lesson Presentation Lesson.
4-5 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
4-5 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
Holt McDougal Geometry 4-5 Triangle Congruence: SSS and SAS 4-5 Triangle Congruence: SSS and SAS Holt Geometry Warm Up Warm Up Lesson Presentation Lesson.
Chapter congruent triangle : SSS and SAS. SAT Problem of the day.
Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL Warm Up 1. What are sides AC and BC called? Side AB? 2. Which side is in between A and C? 3.
Apply SSS and SAS to construct triangles and solve problems. Prove triangles congruent by using SSS and SAS. Objectives.
Warm Up 1. What are sides AC and BC called? Side AB?
 TEKS Focus:  (6)(B) Prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Side-Side- Side, Angle-Angle-Side, and Hypotenuse-Leg.
4.7 ASA and AAS Objectives: Apply ASA and AAS to construct triangles and to solve problems. Prove triangles congruent by using ASA and AAS.
4-6 Warm Up Lesson Presentation Lesson Quiz
4-4 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
Holt McDougal Geometry 4-6 Triangle Congruence: ASA, AAS, and HL Angle Side Angle, Angle Angle Side Triangle Congruence.
Holt McDougal Geometry 4-6 Triangle Congruence: ASA, AAS, and HL 4-6 Triangle Congruence: ASA, AAS, and HL Holt Geometry Warm Up Warm Up Lesson Presentation.
4-3 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
Objectives Apply ASA, AAS, and HL to solve problems.
4.7 ASA and AAS Objectives:
4-5 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
4-5 Warm Up Lesson Presentation Lesson Quiz
4-4 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
4-5 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
Geometry A Bellwork 3) Write a congruence statement that indicates that the two triangles are congruent. A D B C.
4-6 Warm Up Lesson Presentation Lesson Quiz
Objectives Apply SSS and SAS to construct triangles and solve problems. Prove triangles congruent by using SSS and SAS.
4-5 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
Triangle Congruence: SSS and SAS
Objectives Apply ASA, AAS, and HL to construct triangles and to solve problems. Prove triangles congruent by using ASA, AAS, and HL.
4-6 Warm Up Lesson Presentation Practice
4-5 Warm Up Lesson Presentation Lesson Quiz
4-5 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
4-5 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
4-6 Warm Up Lesson Presentation Lesson Quiz
4-6 Warm Up Lesson Presentation Practice
4-5 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
4-6 Warm Up Lesson Presentation Lesson Quiz
4-4 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
Warm Up 1. Name the angle formed by AB and AC.
Learning Targets I will apply the SSS and SAS Postulates to construct triangles and solve problems. I will prove triangles congruent by using the SSS and.
4-6 Warm Up Lesson Presentation Lesson Quiz
4-5 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
5.6 Vocabulary Included Side ASA Triangle Congruence
Warm Up Lesson Presentation Lesson Quiz
Module 1 Topic D – Lesson 24 Warm Up
4-5 Warm Up Lesson Presentation Lesson Quiz
4-4 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
Objectives Apply ASA, AAS, and HL to solve problems.
4-4 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
4-5 Warm Up Lesson Presentation Lesson Quiz
4-4 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
4-4 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
4-4 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
4-5 Warm Up Lesson Presentation Lesson Quiz
Objectives Apply SAS to construct triangles and solve problems.
4-6 Warm Up Lesson Presentation Lesson Quiz
Objectives Apply SSS to construct triangles and solve problems.
4-5 Warm Up Lesson Presentation Lesson Quiz
4-5 Triangle Congruence: SSS and SAS Warm Up Lesson Presentation
Presentation transcript:

CONGRUENT TRIANGLES

How To Find Congruent Sides ? ? Remember to look for the following: Adjacent triangles share a COMMON SIDE, so you can apply the REFLEXIVE Property to get a pair of congruent sides. Look for segment bisectors.. They lead to midpoints…. Which lead to congruent segments.

Use SSS  to explain why ∆ABC  ∆CDA. AB  CD and BC  DA Given AC  CA Reflexive ∆ABC  ∆CDA SSS 

An included angle is an angle formed by two adjacent sides of a polygon. B is the included angle between

How To Find Congruent ANGLES ? ? Remember to look for the following: Look for VERTICAL ANGLES. Look for lines. They form  adjacent angles. Look for // LINES CUT BY A TRANSVERSAL. They lead to  angles. Look for < bisectors. They lead to  angles.

The letters SAS are written in that order because the congruent angles must be INCLUDED between pairs of congruent corresponding sides.

XZY  VZW VERTICAL <‘s are  Engineering Application The diagram shows part of the support structure for a tower. Use SAS  to explain why ∆XYZ  ∆VWZ. XZ  VZ YZ  WZ Given XZY  VZW VERTICAL <‘s are  ∆XYZ  ∆VWZ SAS .

An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side.

When using ASA  , the side must be INCLUDED between the angles known to be congruent.

Determine if you can use ASA  to prove NKL  LMN. Explain. KL and NM are //. KLN  MNL, because // lines imply  alt int >s. NL  LN by the Reflexive Property. No other congruence relationships can be determined, so ASA  cannot be applied.

When using AAS  , the sides must be NONINCLUDED and opposite corresponding angles.

Use AAS  to prove the triangles  Given: JL bisects KLM K  M Prove: JKL  JML JL bisects KLM K  M Given JL  JL Reflexive KLJ  MLJ Def. < bis. JKL  JML AAS 

When using HL  , you must FIRST state that there is a RIGHT TRIANGLE!

Determine if you can use the HL Congruence Theorem to prove ABC  DCB. AC  DB Given ABC & DCB are right angles Given BC  CB Reflexive ABC & DCB are rt. s Def. right   ABC   DCB HL.

Ways to prove  triangles SSS SAS HL ASA AAS