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

Slides:

Advertisements

Similar presentations

Entry task Socractive Multiple Choice

Advertisements

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

4-5 Warm Up Lesson Presentation Lesson Quiz

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.

Congruence in Right Triangles

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

4.3: Analyzing Triangle Congruence

EXAMPLE 4 Use the Third Angles Theorem Find m BDC. So, m ACD = m BDC = 105° by the definition of congruent angles. ANSWER SOLUTION A B and ADC BCD, so.

& 5.2: Proving Triangles Congruent

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,

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.

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

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 M.11.C B

Congruence in Right Triangles

Exploring Congruent Triangles. Congruent triangles: Triangles that are the same size and shape – Each triangle has six parts, three angles and three sides.

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.

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

Isosceles Triangle ABC Vertex Angle Leg Base Base Angles.

4.6: Isosceles and Equilateral Triangles

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

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.

Isosceles Triangle Theorem (Base Angles 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.

Congruency and Triangles Featuring Right Triangles Section 4.6.

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

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

Congruent Triangles Part 2

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.

Unit 1B2 Day 12.   Fill in the chart: Do Now Acute Triangle Right Triangle Obtuse Triangle # of Acute Angles # of Right Angles # of Obtuse Angles.

Solve for x and y: 43° 75° y° x° 75° = y + 43° 75 – 43 = y 32° = y z° x and 43° are Alternate Interior Angles 43° = x.

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.

Geometry-Part 7.

Bell Work: List 3 triangle congruence theorems

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

Congruence in Right Triangles

SSS & hl Congruence Section 5.5.

EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem Write a proof.

Section 4.6 Hypotenuse-Leg

5.5 Proving Triangle Congruence by SSS

5.5 Proving Using SSS.

Lessons 4-4 and 4-5 Proving Triangles Congruent.

Identifying types and proofs using theorems

Isosceles, Equilateral, and Right Triangles

Congruence in Right Triangles

4-6 Congruence in Right Triangles

Prove Triangles Congruent by SAS

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

DRILL Given: Prove: B C A D.

(AAS) Angle-Angle-Side Congruence Theorem

Isosceles, Equilateral, and Right Triangles

4.6 Congruence in Right Triangles

4.4 Prove Triangles Congruent by SAS and HL

Objectives Apply HL to construct triangles and to solve problems.

Chapter 4: Congruent Triangles 4.2: Proving Triangles Congruent

Presentation transcript:

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

Lets start off with a definition. The hypotenuse is the side opposite the right angle. h y p o t e n u s e The other two sides are called legs. l e g Remember a right triangle has one right angle.

If the hypotenuse and a leg of a triangle are congruent to the hypotenuse and leg on another triangle, then the two triangles are congruent. Here comes a theorem Hypotenuse-Leg Theorem {HL} BACEDF A B C D E F

Given: ADCB, D and B are right ’s Prove: ADC CBA It’s time for a proof. StatementReason 1. Given 1. AD  CB,  D &  B are rt  ’s 2. Def of rt  ’s 2.  ADC &  CBA are rt  ’s 3. AC  is hypotenuse 3. Def of hyp. 4. reflexive 4. AC  AC A D B C 5.  ADC  CBA 5. HL

Assignment Workbook Page 327 all