In your math notebook show which sides are congruent to prove the triangles are congruent: F.

Slides:

Advertisements

Similar presentations

5.4 Hypotenuse – Leg Congruence Theorem: HL

Advertisements

Proving Triangles Congruent

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.

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

Proving Triangles Congruent

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)

4.3: Analyzing Triangle Congruence

Chapter 4 Test Review.

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,

Right Triangles 4-3B What are the additional congruence theorems used only for right triangles? Which combination of sides for triangles in general cannot.

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

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

Congruence in Right Triangles

Chapter 4: Triangle Congruence Missy McCarthy Okemos High School Math Instructor.

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.

Isosceles Triangle ABC Vertex Angle Leg Base Base Angles.

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

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

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

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.

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

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.

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

Section 4-5 Triangle Congruence AAS, and HL

Proving Triangles Congruent

Triangle Congruence HL and AAS

Proving Triangles Congruent

4.4 Hypotenuse-Leg (HL) Congruence Theorem

Similar and Congruent Figures

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

Proving Triangles Congruent: SSS and SAS

Other Methods of Proving Triangles Congruent

TRIANGLE CONGRUENCE p q r a b c LESSON 16.

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

4.2 APPLY CONGRUENCE AND TRIANGLES

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

Triangle Congruence HL and AAS

Identifying types and proofs using theorems

Essential Question: What do I need to know about two triangles before I can say they are congruent?

4-5 Proving Congruence Included side: the side between the 2 angles used. AB is the included side between angles A and B. BC is the included side between.

Isosceles, Equilateral, and Right Triangles

Proving Triangles Congruent

4-6 Congruence in Right Triangles

Week 5 Warm Up Add theorem 2.1 here next year.

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 Congruent

Proving Triangles are Congruent

4.4 Prove Triangles Congruent by SAS and HL

5-2 Right Triangles Objectives:

Properties of Triangle Congruence

Chapter 4: Triangle Congruence

Proving Triangles Congruent

4-2 Triangle congruence by sss & sas

Presentation transcript:

In your math notebook show which sides are congruent to prove the triangles are congruent: F

Prove Triangles Congruent by SAS and HL

Prove Triangles Congruent by SAS and HL Draw two lines of any length on a paper.

Prove Triangles Congruent by SAS and HL Draw two lines of any length on a paper. Fold the paper in half along the ends of your lines.

Prove Triangles Congruent by SAS and HL Draw two lines of any length on a paper. Fold the paper in half along the ends of your lines. Draw a line along your fold.

Prove Triangles Congruent by SAS and HL Draw two lines of any length on a paper. Fold the paper in half along the ends of your lines. Draw a line along your fold. Are the two triangles congruent?

Prove Triangles Congruent by SAS and HL Draw two lines of any length on a paper. Fold the paper in half along the ends of your lines. Draw a line along your fold. Are the two triangles congruent? The triangles are congruent because they have two congruent sides with a congruent angle in the middle.

Prove Triangles Congruent by SAS and HL Side-Angle-Side (SAS) Postulate:

Prove Triangles Congruent by SAS and HL Side-Angle-Side (SAS) Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

Prove Triangles Congruent by SAS and HL Side-Angle-Side (SAS) Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. In other words:

Prove Triangles Congruent by SAS and HL Side-Angle-Side (SAS) Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. In other words: If the two sides containing the same angle are the same, the triangles are the same.

Prove Triangles Congruent by SAS and HL Side-Angle-Side (SAS) Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. In other words: If the two sides containing the same angle are the same, the triangles are the same.

Prove Triangles Congruent by SAS and HL AB = DE B E A C D F

Prove Triangles Congruent by SAS and HL AB = DE BC = EF B E A C D F

Prove Triangles Congruent by SAS and HL AB = DE BC = EF BAC = EDF B E A C D F

Apply what you know: Parallel sides:

Does the angle have to be between the two congruent sides?

Right triangles:

Right triangles: The sides next to the right angle are called “legs”.

Right triangles: The sides next to the right angle are called “legs”. The side across from the right angle is called the “hypotenuse”.

Right triangles: The sides next to the right angle are called “legs”. The side across from the right angle is called the “hypotenuse”. Hypotenuse-Leg (HL) Congruence Theorem:

Right triangles: The sides next to the right angle are called “legs”. The side across from the right angle is called the “hypotenuse”. Hypotenuse-Leg (HL) Congruence Theorem: If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.

Right triangles: The sides next to the right angle are called “legs”. The side across from the right angle is called the “hypotenuse”. Hypotenuse-Leg (HL) Congruence Theorem: If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent. In other words:

Right triangles: The sides next to the right angle are called “legs”. The side across from the right angle is called the “hypotenuse”. Hypotenuse-Leg (HL) Congruence Theorem: If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent. In other words: If a leg and hypotenuse are the same, the triangles are the same.

Right Triangles

Right Triangles Are these triangles congruent?

Are the roofs of the houses congruent? How do you know? Angles

Are the roofs of the houses congruent? How do you know? B A Put in the angle.

Are the triangles congruent? How do you know? Put in the hypotenuse and leg.

Brandon Roy shoots a shot from the X, and also from the Y Brandon Roy shoots a shot from the X, and also from the Y. How far away does the Y have to be to make the triangles congruent? Draw two triangles showing different placements on the floor.

Do you travel the same distance going up each flight of stairs Do you travel the same distance going up each flight of stairs? How do you know? Put in height of the left of 10 feet and length on the right of 10 Length on the left of 7 and height on the right of 7 feet. Draw a straight up and down line and side to side to show.

Assignment: Pages 243-244 Numbers 3-15 Even, 25-27 All