Advanced Geometry Section 3.8 The HL Postulate

Slides:

Advertisements

Similar presentations

4.5 Proving Δs are  : ASA and AAS & HL

Advertisements

Proving Triangles Congruent

4.6 Congruence in Right Triangles

7-5 The SSA Condition and HL Congruence

HL Postulate Lesson 3.8.

Hypotenuse – Leg Congruence Theorem: HL

4.4 – Prove Triangles Congruent by HL

3.8 The HL Postulate Objective:

1 MM1G3c Proving Triangles Congruent (AAS, HL). 2 Postulates AAS If two angles and a non included side of one triangle are congruent to the corresponding.

4.6: Congruence in Right Triangles

Proving Triangles Congruent Advanced Geometry Triangle Congruence Lesson 2.

ADVANCED GEOMETRY 3.1/2 What are Congruent Figures? / Three ways to prove Triangles Congruent. Learner Objective: I will identify the corresponding congruent.

ADVANCED GEOMETRY 3.6 Types of Triangles LEARNER OBJECTIVE: Students will classify triangles by sides and by angles and will complete problems and proofs.

TODAY IN GEOMETRY…  Go over proofs from HW #5  4.4 WS Warm Up  Learning Goal: 4.5 You will use postulates Angle-Side-Angle and Angle-Angle-Side to prove.

4.5 Even Answers.

Notes Over Congruence When two polygons are ___________their corresponding parts have the _____ _______. congruent same measure 1. Name the corresponding.

4-6 Congruence in Right Triangles M.11.C B

Proving Triangles Congruent

Congruence in Right Triangles

4.6 Congruence in Right Triangles In a right triangle: – The side opposite the right angle is called the hypotenuse. It is the longest side of the triangle.

Warm up. 4.3 Analyzing Triangle Congruence Two new shortcuts: AAS HL.

Big Idea: Prove Triangles are Congruent by SAS and HL.

TargetDueAssignment 4.51/15p. 257: 11, 12, 14-18, 22, 24, Objectives Apply ASA, AAS, and HL to construct triangles and to solve problems. Prove triangles.

4.6 Congruence in Right Triangles To Prove Triangles Congruent using the Hypotenuse Leg Theorem.

Δ CAT is congruent to Δ DOG. Write the three congruence statements for their SIDES

By Shelby Smith and Nellie Diaz. Section 8-1 SSS and SAS  If three sides of one triangle are congruent to three sides of another triangle, then the triangles.

TODAY IN GEOMETRY…  REVIEW: SSS, SAS, HL, ASA, AAS  WARM UP: PROOF-A-RAMA 1  Learning Goal: 4.6 Use CPCTC to prove congruent parts of a triangle  Independent.

ASA AND AAS CONGRUENCE Section 4.5. Angle-Side-Angle (ASA) Congruence Postulate  If two angles and the included side of one triangle are congruent to.

Objectives Apply ASA, AAS, and HL to construct triangles and to solve problems. Prove triangles congruent by using ASA, AAS, and HL.

Warm-Up Are the 2 triangle congruent? If so, write the theorem or postulate that proves them congruent. Write a congruency statement. A D C B.

Triangle Proofs. USING SSS, SAS, AAS, HL, & ASA TO PROVE TRIANGLES ARE CONGRUENT STEPS YOU SHOULD FOLLOW IN PROOFS: 1. Using the information given, ______________.

Warm Up 1.) Find the measure of the exterior angle.

Triangle Congruence Theorems

Prove triangles congruent by ASA and AAS

Geometry-Part 7.

4-2 Triangle Congruence by SSS and SAS

Section 4-5 Triangle Congruence AAS, and HL

Proving Triangles Congruent

Triangle Congruence HL and AAS

Triangle Congruence Theorems

4.4 Hypotenuse-Leg (HL) Congruence Theorem

5.3 Proving Triangles are congruent:

Proving Triangles Congruent: SSS and SAS

Other Methods of Proving Triangles Congruent

Proving Triangles Congruent

Proving Triangles Congruent

Warm-Up Determine if the following triangles are congruent and name the postulate/definitions/properties/theorems that would be used to prove them congruent.

More Proving Triangles Congruent

Section 21.3: HL Triangle Congruence

Triangle Congruence HL and AAS

Identifying types and proofs using theorems

Proving Triangles Congruent

Triangle Congruence Theorems

Triangle Congruence Theorems

Congruence in Right Triangles

4-6 Congruence in Right Triangles

Prove Triangles Congruent by SAS

Postulates and Theorems to show Congruence SSS: Side-Side-Side

(AAS) Angle-Angle-Side Congruence Theorem

4.6 Congruence in Right Triangles

Proving Triangles are Congruent

Triangle Congruence Theorems

Properties of Triangle Congruence

Chapter 4: Triangle Congruence

Warm Up 1 ( Write a congruence statement

3.5 Overlapping Triangles

8.3 Methods of Proving Triangles are Similar Advanced Geometry 8.3 Methods of Proving    Triangles are Similar Learner Objective: I will use several.

Learner Objective: Students will write paragraph proofs.

4.2 /4.3 – Triangle Congruence

Presentation transcript:

Advanced Geometry Section 3.8 The HL Postulate Learner Objective: Students will solve proofs and problems using  the HL Postulate of triangle congruence.

Warm Up Statement Reason

How can we prove that triangles are congruent?

What about SSA? In these triangles, two pairs of corresponding sides and a NON-INCLUDED  pair of corresponding angles are congruent. Do the triangles appear to be congruent?

There is one special case when SSA does prove triangles are congruent There is one special case when SSA does prove triangles are  congruent. This occurs when the corresponding angles are RIGHT  ANGLES which makes the congruent sides a HYPOTENUSE and a  LEG of the RIGHT triangle.

H-L Postulate If there exists a correspondence between the vertices of   two RIGHT TRIANGLES such that the Hypotenuse and a Leg of one triangle are congruent to   the corresponding parts of the other triangle, then the two RIGHT TRIANGLES are congruent. ONLY APPLIES TO RIGHT TRIANGLES!

STATEMENTS REASONS Given: Prove: bisects A C B D

Prove: Corresponding angle bisectors of congruent triangles are   congruent. STATEMENTS REASONS D E F H A B C G Given: Prove: bisects

HW: Pg. 158 # 1,2,6,7,10,12,15