Hypotenuse Leg (HL). Other Possibilities? SSA 30  Will this ever Work?

Slides:

Advertisements

Similar presentations

Proving Triangles Congruent

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

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.

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

The Pythagorean Theorem. The Right Triangle A right triangle is a triangle that contains one right angle. A right angle is 90 o Right Angle.

Lesson 56: Special 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.

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.

Aim: Triangle Congruence – Hyp-Leg Course: Applied Geometry Do Now: Aim: How to prove triangles are congruent using a 5 th shortcut: Hyp-Leg. In a right.

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

Section 8.4 Special Right Triangles VERY VERY VERY VERY IMPORTANT SAT SECTION.

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

Proving Triangles Congruent

Congruence in Right Triangles

3.8 HL Objectives: Use HL in proofs to prove triangles congruent.

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle.

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.

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.

What information is missing to say that: a.ΔTUW  ΔQOS by SAS b. ΔTUW  ΔQOS by AAS.

4-5 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: 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.

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

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

Bell-Ringer Given:, m

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.

Special Right Triangles

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

Warm Up m<L = m<L = 180 m<L =

Proving Triangles Congruent

b. ΔTUW  ΔQOS by AAS ΔTUW  ΔQOS by SAS ∠T  ∠Q TU  QO

Triangle Congruence HL and AAS

4.4 Hypotenuse-Leg (HL) Congruence Theorem

8-2 Special Right triangles

Other Methods of Proving Triangles Congruent

Proving Triangles Congruent

Proving Triangles Congruent

Modules 5 & 6 Triangle Congruence Proofs

More Proving Triangles Congruent

Congruence of Triangles 4.1, 4.2, 4.3, 4.5, 4.6

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?

Proving Triangles Congruent

Triangle Congruence Theorems

4-6 Congruence in Right Triangles

6.5 Pythagorean Theorem.

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

Modules 5 & 6 Triangle Congruence Proofs

DRILL Given: Prove: B C A D.

(AAS) Angle-Angle-Side Congruence Theorem

Proving Triangles are Congruent

Triangle Congruency Theorems (shortcuts)

5-2 Right Triangles Objectives:

The Pythagorean Theorem

Warm Up You will need your own paper for part of the lesson. Simplify:

Proving Triangles Congruent

7-3 Special Right Triangles

Presentation transcript:

Hypotenuse Leg (HL)

Other Possibilities? SSA 30  Will this ever Work?

Special Case of SSA Given a right angle, one leg, & the hypotenuse - Does this prove the triangles congruent? S S A

Yes – Remember Pythagorean Theorem a 2 + b 2 = c 2 c b a b’ a’ c’

a 2 + b 2 = c 2 Because of Pythagorean thm. a must = a’ This gives SSS  5 3 a 3 a’ 5

HL  Theorem If the hyp & leg of one right /\ are  to the hyp & leg of another right /\ then the /\ are 

Exercise 21 Given: <A  <D AF  DC AC  DF <BFA  <ECD Prove: /\ AFB  /\ DCE A E F B C D

Exercise 22 Given: <1  <4 AF  DC <A  <D Prove: /\ AFB  /\ DCE A E F B C D