Given: DB bisects AE <D = <B Prove: AD = BE AB C D E Given Definition of Bisector Vertical Angle Theorem ?? DB bisects AE DC = CB <ACD = <ECB ? ΔACD =

Slides:



Advertisements
Similar presentations
Proving Triangles Congruent
Advertisements

4.6 Using Congruent Triangles
Chapter 4.6 Notes: Use Congruent Triangles Goal: You will use congruent triangles to prove that corresponding parts are congruent.
TODAY IN GEOMETRY…  Review: Finding congruent angles and sides and proving triangles are congruent.  Learning Goal: 4.6 Use CPCTC to prove congruent.
Module 5 Lesson 2 – Part 2 Writing Proofs
What are the ways we can prove triangles congruent? A B C D Angle C is congruent to angle A Angle ADB is congruent to angle CDB BD is congruent to BD A.
Use right angle 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.
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.
HOMEWORK: Lesson 4.6/1-9, 18 Chapter 4 Test - FRIDAY
Isosceles Triangles Geometry D – Chapter 4.6. Definitions - Review Define an isosceles triangle. A triangle with two congruent sides. Name the parts of.
5.1 Perpendiculars and Bisectors Geometry Mrs. Spitz Fall 2004.
Section 5-2 Bisectors in Triangles. Vocabulary Distance from a point to a line: the length of the perpendicular segment from the point to the line.
Inequalities Involving Two Triangles SAS Inequality/Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle and the included.
EXAMPLE 3 Write a flow proof In the diagram, CE BD and  CAB CAD. Write a flow proof to show ABE ADE GIVEN CE BD,  CAB CAD PROVE ABE ADE.
Unit 4 Proving Triangles Congruent (SSS, SAS, ASA, AAS, HL)
Using Congruent Triangles Class Worksheet Part 2.
Give reasons for each step in this proof. B D A E C Given: C is the midpoint of AC, C is the midpoint of DB Prove: AB is congruent to ED StatementsReasons.
5.1 midsegments of triangles Geometry Mrs. Spitz Fall 2004.
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.
AAS examples By: Ana Cristina Andrade. A D C E V V Given: segment AD is parallel to segment BC. Segment AD is congruent to segment CB Proof: Triangle.
Geometry: Partial Proofs with Congruent Triangles.
Isosceles Triangle Theorem (Base Angles Theorem)
Triangle Congruences SSS SAS AAS ASA HL.
Δ CAT is congruent to Δ DOG. Write the three congruence statements for their SIDES
By Shelby Smith and Nellie Diaz. Section 8-1 SSS and SAS  If three sides of one triangle are congruent to three sides of another triangle, then the triangles.
Chapter 4 Review Cut-n-Paste Proofs. StatementsReasons SAS Postulate X is midpoint of AC Definition of Midpoint Given Vertical Angles Theorem X is midpoint.
4-4 Using Corresponding Parts of Congruent Triangles I can determine whether corresponding parts of triangles are congruent. I can write a two column proof.
Isosceles and Equilateral Triangles
LESSON 5-3 MEDIANS, ALTITUDES & ANGLE BISECTORS OF TRIANGLES
7-3 Triangle Similarity I CAN -Use the triangle similarity theorems to
5.1 Perpendiculars and Bisectors
SAS SSS SAS SSS.
Aim: How do we prove triangles congruent using the Angle-Angle-Side Theorem? Do Now: In each case, which postulate can be used to prove the triangles congruent?
6-2 Properties of Parallelograms
Objective! Use CPCTC to prove parts of triangles are congruent.
Does the diagram give enough information to show that the
Chapter 2.6 (Part 1): Prove Statements about Segments and Angles
Use right angle congruence
Warm Up (on the ChromeBook cart)
2 Column PROOFS.
The Isosceles Triangle Theorems
Class Greeting.
Flow Chart.
Two-Column Triangle Proofs
Proving Triangles Congruent Corresponding parts of congruent triangles
Objective! Use CPCTC to prove parts of triangles are congruent.
4-7 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC
4.4 Proving Triangles are Congruent by ASA and AAS
Check your answers from 5.2 (p )
Objective: To use and apply properties of isosceles triangles.
Proving Triangles Congruent
Warm Up (on handout).
Aim: Do Now: ( ) A B C D E Ans: S.A.S. Postulate Ans: Ans:
Geometry Proofs Unit 12 AA1.CC.
Chapter 4 Lesson 3 Objective: To prove two triangles congruent using the ASA Postulate and the AAS Theorem.
CPCTC uses congruent triangles to prove corresponding parts congruent.
Proving Triangles Congruent
4-7 & 10-3 Proofs: Medians Altitudes Angle Bisectors Perpendicular
Bell Work Complete problems 8, 9, and 15 from yesterday. Proofs are on the board.
Proving Triangles Congruent
Postulates and Theorems to show Congruence SSS: Side-Side-Side
Ex: Given: Prove: CPCTC:
Proving Triangles Congruent
Pearson Unit 1 Topic 4: Congruent Triangles 4-7: Congruence in Overlapping Triangles Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007.
4.1 Detours and Midpoints Objectives: To use detours in proofs and to apply the midpoint formula.
Chapter 5: Quadrilaterals
Warm Up 7.4 Is there enough information to prove that the triangles are congruent? If so, state the reason (SSS, SAS, HL, ASA,
Other Methods of Proving Triangles Congruent
Presentation transcript:

Given: DB bisects AE <D = <B Prove: AD = BE AB C D E Given Definition of Bisector Vertical Angle Theorem ?? DB bisects AE DC = CB <ACD = <ECB ? ΔACD = ΔECBAD = BE Why is this wrong and fix it. Fill in missing reason. Fill in missing statement.

Given: DB bisects AE <D = <B Prove: AD = BE AB C D E Given Definition of Bisector Vertical Angle Theorem AAS postulateCPCTC DB bisects AE AC = CE <ACD = <ECB <D = <B ΔACD = ΔECBAD = BE Why is this wrong and fix it. Fill in missing reason. Fill in missing statement. AE gets cut in half not DB Other given is seen above Explain by marking on picture CPCTC always used to prove a part is congruent after proving congruent triangles A S A ANSWER KEY

Given: <D & <B are right angles <DAE = <BEA Prove: AD = BE AB D E Given CPCTC ? ? <D & <B are right angles <D = <B AE = AE ? ΔADE = ΔEBAAD = BE Why is this wrong and fix it. Fill in missing reason. Fill in missing statement. Definition of Right Angle

Given: <D & <B are right angles <DAE = <BEA Prove: AD = BE AB D E Given CPCTC AAS Reflexive Property <D & <B are right angles <D = <B AE = AE <DAE = <BEA ΔADE = ΔEBAAD = BE Why is this wrong and fix it. Fill in missing reason. Fill in missing statement. Right Angle Theorem ANSWER KEY A S A Other given is seen above Using a shared piece. It is a theorem not a definition. Def of Right Angle = right angle is 90 Explain by marking on picture

Congruent Triangle Proof Oral Test Rubric Congruent Triangle Proof Oral Test Student correctly completed 1 items in proof. Each item was correctly & clearly explained. Student correctly completed 2 items. However explanatio ns were not clear or only partially correct. Student correctly completed 2 items in proof. Each item was correctly & clearly explained. Student correctly completed 3 items. However explanatio ns were not clear or only partially correct. Student correctly completed 3 items in proof. Each item was correctly & clearly explained. Student correctly completed all 4 items. However explanatio ns were not clear or only partially correct. Student correctly completed all 4 items including filling in 3 missing items & correcting error in proof. Each item was correctly & clearly explained.