Identifying types and proofs using theorems

Slides:

Advertisements

Similar presentations

4.5 Proving Δs are  : ASA and AAS & HL

Advertisements

Proving Triangles Congruent

5.4 Hypotenuse – Leg Congruence Theorem: HL

Proving Triangles Congruent

Hypotenuse – Leg Congruence Theorem: HL

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.

WARM UP 1)List the six congruencies if the following is true. 2)Plot the points and locate point C so that F(7,5) A(-2,2) T(5,2)

Chapter 4.5 Notes: Prove Triangles Congruent by ASA and AAS Goal: You will use two more methods to prove congruences.

Chapter 4: Congruent Triangles Objective: To recognize congruent triangles and their corresponding parts. Key Vocabulary: Congruent Triangles.

Proving Triangles Congruent. Warm Up Objectives Can you prove triangles congruent using SSS, SAS, ASA, AAS, and HL?

Do Now #28:. 5.4 Hypotenuse-Leg (HL) Congruence Theorem Objective: To use the HL Congruence Theorem and summarize congruence postulates and theorems.

Geometry 4-5 ASA, AAS, and HL. Vocab. Word An included side is the common side of two consecutive angles in a polygon. (The side in between two angles)

Proving Triangles Congruent

Congruence in Right Triangles

DO NOW!!! Solve for “x”..

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.

GE = 2x – 7 GF = x + 4. What is GD? Solve for the variable Bellringer P 23 top 10 lines.

Unit 2 Part 4 Proving Triangles Congruent. Angle – Side – Angle Postulate If two angles and the included side of a triangle are congruent to two angles.

4-3 Triangle Congruence by ASA and AAS. Angle-Side-Angle (ASA) Postulate If two angles and the included side of one triangle are congruent to two angles.

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

5.6 Proving Triangle Congruence by ASA and AAS. OBJ: Students will be able to use ASA and AAS Congruence Theorems.

Proving Triangle Congruency. What does it mean for triangles to be congruent? Congruent triangles are identical meaning that their side lengths and angle.

Are the following triangles congruent? Why or why not? Write a congruence statement for the triangles. 21 ° 74 ° 85 ° 21 ° 74 ° 85 ° T S R L M N.

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

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

Triangle Congruence Theorems

Prove triangles congruent by ASA and AAS

Geometry-Part 7.

Section 4-5 Triangle Congruence AAS, and HL

Proving Triangles are Congruent

Proving Triangles Congruent

Triangle Congruence HL and AAS

Aim: How do we prove triangles congruent using the Angle-Angle-Side Theorem? Do Now: In each case, which postulate can be used to prove the triangles congruent?

Triangle Congruence Theorems

4.4 Hypotenuse-Leg (HL) Congruence Theorem

Right Triangles What are the additional congruence theorems used only for right triangles? Which combination of sides for triangles in general cannot.

5.3 Proving Triangles are congruent:

Proving Triangles Congruent: SSS and SAS

Other Methods of Proving Triangles Congruent

Proving Triangles Congruent

Proving Triangles Congruent

Proving Triangles Congruent

Three ways to prove triangles congruent.

4-4 and 4-5: Congruent Triangle Theorems

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

4-2 Some Ways to Prove Triangles Congruent (p. 122)

Triangle Congruence Theorems

Triangle Congruence HL and AAS

CONGRUENT TRIANGLES 2 Triangles are CONGRUENT if they have:

4.1 Congruent Figures -Congruent Polygons: have corresponding angles and sides -Theorem 4.1: If 2 angles of 1 triangle are congruent to 2 angles of another.

Triangle Congruence Theorems

Proving Triangles Congruent

Triangle Congruence Theorems

Learn to use the ASA and AAS tests for congruence.

Triangle Congruence Theorems

4-6 Congruence in Right Triangles

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 Congruency Theorems (shortcuts)

Triangle Congruence Theorems

5-2 Right Triangles Objectives:

Properties of Triangle Congruence

Warm Up 7.4 Is there enough information to prove that the triangles are congruent? If so, state the reason (SSS, SAS, HL, ASA,

Warm Up 1 ( Write a congruence statement

4-4/4-5 Proving Triangles Congruent

Proving Triangles Congruent

4.2 /4.3 – Triangle Congruence

Presentation transcript:

Identifying types and proofs using theorems Triangle congruence Identifying types and proofs using theorems

(ASA) Angle-Side-Angle Congruence Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent.

Side-Angle-Side (SAS) Postulate If two sides and the included angle of one triangle is congruent to two sides and the included angle of another triangle, then the two triangles are congruent. B A C X Y Z ) (

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. E D F A B C

(AAS) Angle-Angle-Side Congruence Theorem If two angles and a non- included side of one triangle are congruent to two angles and the corresponding non- included side of a second triangle, then the triangles are congruent.

(HL) Hypotenuse - Leg  Theorem If the hypotenuse and a leg of a right Δ are  to the hypotenuse and a leg of a second Δ, then the 2 Δs are . (HL) Hypotenuse - Leg  Theorem