4.6 Congruence in Right Triangles

Slides:

Advertisements

Similar presentations

5.4 Hypotenuse – Leg Congruence Theorem: HL

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

4-6 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

Congruence in Right Triangles

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.

4.6 The Isosceles Triangle Theorems Base Angles and Opposite Sides Hypotenuse - Leg.

4.5 Even Answers.

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

30°, 60°, and 90° - Special Rule The hypotenuse is always twice as long as the side opposite the 30° angle. 30° 60° a b c C = 2a.

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

Proving Triangles Congruent

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.

Isosceles Triangle ABC Vertex Angle Leg Base Base Angles.

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

4.6: Isosceles and Equilateral Triangles

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

Triangle Sum Theorem The sum of the angle measures in a triangle is 180 degrees.

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.

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.

Warm-up AAS SSS Not possible HL Not possible SAS.

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.

Pythagorean Theorem Converse Special Triangles. Pythagorean Theorem What do you remember? Right Triangles Hypotenuse – longest side Legs – two shorter.

4.3 TRIANGLE CONGRUENCE BY ASA AND AAS TO PROVE TRIANGLE CONGRUENCE BY ASA POSTULATE AND AAS THEOREM.

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.

Sect. 4.6 Isosceles, Equilateral, and Right Triangles

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

Triangle Congruence Theorems

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.

Other Methods of Proving Triangles Congruent

Proving Triangles Congruent

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.

Triangle Congruence Theorems

Isosceles, Equilateral, and Right Triangles

4-6 Congruence in Right Triangles

(AAS) Angle-Angle-Side Congruence Theorem

Isosceles, Equilateral, and Right Triangles

4.6 Congruence in Right Triangles

Proving Triangles are Congruent

Triangle Congruency Theorems (shortcuts)

Properties of Triangle Congruence

Lesson 3-2 Isosceles Triangles.

Chapter 4: Triangle Congruence

Lesson 3-2 Isosceles Triangles.

Proving Triangles Congruent

Advanced Geometry Section 3.8 The HL Postulate

Presentation transcript:

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

Right Triangles… In a Right Triangle the side opposite the Right Angle is called the Hypotenuse. The Hypotenuse is always the largest side of the Right Triangle The other two sides are called the Legs. The Legs will always include the Right Angle.

Side Side Angle? Remember SSA is not a Congruence Rule in All Triangles. It does work however in a special case, Right Triangles. It occurs when hypotenuses and one pair of legs are congruent.

The HL Theorem!

So… To Use the HL Theorem, you must show that three conditions are met: There are two right triangles. (Right Angles) The triangles have congruent hypotenuses. There is one pair of congruent legs.

Example 1B What two triangles are congruent by the Hypotenuse Leg (HL) Theorem? Write a Congruence Statement… ∆LMN ≅ ∆OQP

Example 2: Using HL Theorem

Example 3: Using HL Theorem

Closure… How are SAS and HL Theorem alike? How are they Different? How does AAS Relate to HL Theorem? (Think Isosceles Triangles…)