4.2: Triangle Congruency by SSS and SAS Objectives: To prove two triangles congruent using the SSS and SAS Postulates.

Slides:

Advertisements

Similar presentations

Hypotenuse – Leg Congruence Theorem: HL

Advertisements

6-2: Proving Congruence using congruent parts Unit 6 English Casbarro.

Congruent Polygons Have congruent corresponding parts. Have congruent corresponding parts. When naming congruent polygons, always list corresponding vertices.

Section 4-3 Triangle Congruence (ASA, AAS) SPI 32C: determine congruence or similarity between triangles SPI 32M: justify triangle congruence given a diagram.

4.4 & 4.5 Proving Triangles Congruent

4-4 & 4-5: Tests for Congruent Triangles

Proving Triangles Congruent

Proving Triangles Congruent Advanced Geometry Triangle Congruence Lesson 2.

Chapter 4. Congruent Figures – figures that have exactly the same size and shape.Congruent Figures – figures that have exactly the same size and shape.

Chapter 4.5 Notes: Prove Triangles Congruent by ASA and AAS Goal: You will use two more methods to prove congruences.

4.5 – Prove Triangles Congruent by ASA and AAS

Chapter 4: Congruent Triangles Objective: To recognize congruent triangles and their corresponding parts. Key Vocabulary: Congruent Triangles.

4.3 & 4.4 Proving Triangles are Congruent

Triangle Congruence Postulates T.2.G.1 Apply congruence (SSS …) and similarity (AA …) correspondences and properties of figures to find missing parts of.

Triangle Congruence Students will be able to apply the Triangle Congruence Postulates in order to solve problems.

4-2: Triangle Congruence by SSS and SAS 4-3: Triangle Congruence by ASA and AAS 4-4: Using Corresponding Parts of Congruent Triangles.

Proving Triangles Congruent Geometry Ch 04 A BowerPoint Presentation.

Geometry – Chapter 4 Congruent Triangles.

Proving Triangles Congruent. Warm Up Objectives Can you prove triangles congruent using SSS, SAS, ASA, AAS, and HL?

Chapter 4: Congruent 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,

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

Triangle Congruence: SSS, SAS, ASA, AAS, and HL

4.1: Apply Triangle Sum Properties

Chapter 4 Notes Classify triangles according to their sides

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)

Proving Triangles Congruent

Congruence in Right Triangles

DO NOW!!! Solve for “x”..

(4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AAS Learning Target: To be able to prove triangle congruency by SSS, SAS, ASA, or AAS using proofs.

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

Monday, October 22, 2012 Homework: p. 211 #28-34 even.

WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.

Congruent Triangles have six sets of corresponding parts! Three sets of corresponding sides Three sets of corresponding angles.

4.3 Triangle Congruence by ASA and AAS You can prove that two triangles are congruent without having to show that all corresponding parts are congruent.

8-3 Proving Triangles Similar M11.C B

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.

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

Chapter 4.1 Common Core - G.SRT.5 Use congruence…criteria for triangles to solve problems and prove relationships in geometric figures. Objectives – To.

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

4-2 Triangle Congruence by SSS and SAS. Side-Side-Side (SSS) Postulate If the three sides of one triangle are congruent to the three sides of another.

Triangle Congruency Classifying Triangles by Sides Equilateral Triangle 3 congruent sides Isosceles Triangle At least 2 congruent sides Scalene 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.

4.2: Triangle Congruency by SSS and SAS

For 9 th /10 th grade Geometry students Use clicker to answer questions.

4-3 Triangle Congruence by ASA and AAS. Angle-Side-Angle (ASA) Postulate If two angles and the included side of one triangle are congruent to two angles.

DO NOW Identify the corresponding parts using tick marks. Then state which polygons are congruent. 1.2.

4.4 Proving Triangles are Congruent: ASA and AAS Geometry.

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

Drill Write your homework in your planner Take out your homework What postulate would you use to prove the triangles below congruent?

Are the following triangles congruent? Why or why not? Write a congruence statement for the triangles. 21 ° 74 ° 85 ° 21 ° 74 ° 85 ° T S R L M N.

Geometry. Congruent polygons have corresponding sides that are congruent and corresponding angles that are congruent.

Bell Work 12/12 State which two triangles, if any, are congruent, and write a congruence statement and reason why 1) 2) Solve for the variables 3) 4)

Objectives: To recognize congruent figures and their corresponding parts.

Do Now: Identify two congruent triangles in the figure below. H N A D.

Objectives Apply ASA, AAS, and HL to construct triangles and to solve problems. Prove triangles congruent by using ASA, AAS, and HL.

Congruent Triangles Unit 4-5 Congruent Triangle Theorems.

Do-Now 2) Find the value of x & the measure of each angle. 5x – 4 4x ° 1) Find the value of x. 4x x – 10 3x + 1 5x – 4 + 4x + 14 = 100 9x.

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.

Side-side-side (SSS) postulate If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Warm Up: March 27th Translate Left 5 and down 4Left 3 and up 2 A B CD.

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

Other Methods of Proving Triangles Congruent

Proving Triangles Congruent

Identifying types and proofs using theorems

4-6 Congruence in Right Triangles

(AAS) Angle-Angle-Side Congruence Theorem

Proving Triangles are Congruent

4-4/4-5 Proving Triangles Congruent

Presentation transcript:

4.2: Triangle Congruency by SSS and SAS Objectives: To prove two triangles congruent using the SSS and SAS Postulates.

Side-Side-Side (SSS)Postulate If 3 sides of one triangle are to 3 sides of another triangle, then the triangles are. (Notice the order in which the congruency statement is given)

A B C D 1.Which other side do we know is congruent? Why? 2.Which two triangles are congruent? 3. How do you know?

Included Angles and Sides B N X is included between Angle B and Angle X is included between NB and NX. Which side is included between angle N and angle B? Which angle is included between BX and NX?

Side-Angle-Side (SAS) Postulate If 2 sides and the included angle of one triangle are to 2 sides and the included angle of another triangle, then the 2 triangles are. Again, notice the order of the congruency statement.

Name the triangle congruence postulate, if any, that you can use to prove each pair of triangles congruent. Then write a congruency statement M M O PQ N L K J RP N A C S

What other information do you need to prove by SSS? D AB C From the information given, can you prove ? Explain. E C D B A

ASA Postulate Angle-Side-Angle If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

AAS Theorem Angle-Angle-Side If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.

Can you prove the triangles are congruent?

HL Hypotenuse-Leg If the hypotenuse and a leg of one right triangle are congruent To the hypotenuse and a leg of another right triangle, then The triangles are congruent.

Can you prove the triangles are congruent ?

History According to legend, one of Napoleon’s officers used congruent triangles to estimate the width of a river. On the riverbank, the officer stood up straight and lowered the visor of his cap until the farthest thing he could see was the edge of the opposite bank. He then turned and noted the spot on his side of the river that was in line with his eye and the tip of his visor.