4-6 Congruence in Right Triangles

Slides:

Advertisements

Similar presentations

4.6 Congruence in Right Triangles

Advertisements

4.4 – Prove Triangles Congruent by SAS and HL Consider a relationship involving two sides, and the angle they form, their included angle. Any time you.

Ways to Prove Triangles Congruent

7-5 The SSA Condition and HL Congruence

Hypotenuse – Leg Congruence Theorem: HL

4.4 – Prove Triangles Congruent by HL

3.8 The HL Postulate Objective:

4-6 Congruence in Right Triangles

4.6: Congruence in Right Triangles

4.4 – Prove Triangles Congruent by SAS and HL Consider a relationship involving two sides, and the angle they form, their included angle. Any time you.

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

Mr. Schaab’s Geometry Class Our Lady of Providence Jr.-Sr. High School

12/16/09 Do Now Label the hypotenuse, legs, and acute angles of the following right triangles. A C B D E.

Right Triangle Congruence

4-6 Congruence in Right Triangles. Notice the triangles are not congruent, so we can conclude that Side-Side-Angle is NOT valid. However Side-Side-Angle,

4.6 Congruence in Right Triangles

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

Isosceles, Equilateral, and Right Triangles Sec 4.6 GOAL: To use properties of isosceles, equilateral and right triangles To use RHL Congruence Theorem.

4.6 Congruence in Right Triangles You will construct and justify statement about right triangles.

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)

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

Congruence in Right Triangles

DO NOW!!! Solve for “x”..

Congruence in Right Triangles Chapter 4 Section 6.

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.

4.9Prove Triangles Congruent by SAS Side-Angle-Side (SAS) Congruence Postulate If two sides and the included angle of one triangle are congruent to two.

Isosceles Triangle ABC Vertex Angle Leg Base Base Angles.

4.6: Isosceles and Equilateral Triangles

Warm Up 12/5/12 State the 6 congruent parts of the triangles below. 10 minutes End.

5.5 Proving Triangle Congruence by SSS OBJ: Students will be able to use Side-Side-Side (SSS) Congruence Theorem and Hypotenuse-Leg (HL) Congruence Theorem.

5.4 Proving Triangle Congruence by SSS

CONGRUENCE IN RIGHT TRIANGLES Lesson 4-6. Right Triangles  Parts of a Right Triangle:  Legs: the two sides adjacent to the right angle  Hypotenuse:

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

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.

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.

Review: Solving Systems x 2y+3 x+y 12 Find the values of x and y that make the following triangles congruent.

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

Prove triangles congruent by ASA and AAS

Geometry-Part 7.

4-2 Triangle Congruence by SSS and SAS

Proving Triangles Congruent

Triangle Congruence HL and AAS

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:

Other Methods of 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.

5.5 Proving Triangle Congruence by SSS

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

Section 21.3: HL Triangle Congruence

SSS and, AAS Triangle Congruence Theorems

Triangle Congruence HL and AAS

Identifying types and proofs using theorems

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.

Isosceles, Equilateral, and Right Triangles

Prove Triangles Congruent by SAS

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

(AAS) Angle-Angle-Side Congruence Theorem

Isosceles, Equilateral, and Right Triangles

4.6 Congruence in Right Triangles

Proving Triangles are Congruent

5-2 Right Triangles Objectives:

Chapter 4: Triangle Congruence

Lesson 3-2 Isosceles Triangles.

Proving Triangles Congruent

Presentation transcript:

4-6 Congruence in Right Triangles Other ways to prove triangles congruent

Working with Right Triangles Before we can use any of these Theorems we must first state that we are working with Right Triangles. How do we know we have a Right Triangle? We must then first identify that some angles are right angles.

Definitions Hypotenuse  in a right triangle it is the side opposite the right angle. Legs the other 2 sides of a right triangle.

HL (Hypotenuse Leg) Theorem If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

Explain how you know that