Warm up No, the measures are not the same Yes, angle measures are the same and the rays go to infinity No, corresponding sides are not congruent, and we.

Slides:

Advertisements

Similar presentations

Proving Triangles Congruent

Advertisements

Hypotenuse – Leg Congruence Theorem: HL

Proving Triangles Congruent

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

But first a little warm up… How much do you need to know? To prove two triangles are exactly alike? (congruent) If all 6 parts (3 corresponding sides.

Similarity & Congruency Dr. Marinas Similarity Has same shape All corresponding pairs of angles are congruent Corresponding pairs of sides are in proportion.

4.4 & 4.5 Proving Triangles Congruent

Congruent Polygons. Congruent segments have the same length.

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)

Proving Triangles Congruent. Two geometric figures with exactly the same size and shape. Review of Congruence A C B DE F.

Lesson 4.4 Triangle Congruencies. Two geometric figures with exactly the same size and shape. The Idea of a Congruence A C B DE F.

Objective: discover conditions to prove triangles are congruent. Two figures are congruent if and only if : one can be mapped onto the other by one or.

Good Morning! Please take out your homework from last night and your 4.4 review worksheet and clear off your desks.

SSS, SAS, and SSA Congruence Shortcuts Objectives: 1. Explore shortcuts for determining whether triangles are congruent.

Warm-up with 4.5 other congruence shortcuts For 1 -3 tell whether it is possible (YES or No) to draw a triangle with the given side lengths. 1) 7 in.,

ADVANCED GEOMETRY 3.1/2 What are Congruent Figures? / Three ways to prove Triangles Congruent. Learner Objective: I will identify the corresponding congruent.

Math 1 February 27 th Turn in homework – page 34.

© 2008 Pearson Addison-Wesley. All rights reserved Chapter 1 Section 9-4 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem.

Proving Triangles Congruent

Notes Over Congruence When two polygons are ___________their corresponding parts have the _____ _______. congruent same measure 1. Name the corresponding.

Lesson: 9 – 3 Similar Triangles

Chapter 5 Introduction to Trigonometry: 5

Geometry 4-3 Triangle Congruence

Proving Triangles Congruent

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

Warm up. Polygon Congruence Polygon Similarity Triangle Congruence Shortcuts Triangle Similarity Shortcuts 1. Need to prove that corresponding angles.

Triangle Congruence. 3 line segments (dried spaghetti sticks – make three different sizes) Take 3 line segments Make a triangle Mark the vertices Draw.

Congruent Triangles Congruency statements and why triangles are congruent.

Warm-Up (#33 p.191). 4.3 Triangle Congruence by ASA and AAS.

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

Drill Write your homework in your planner Take out your homework Find all angle measures:

CHAPTER 4 SECTION 2 Triangle Congruence by SSS and SAS.

Unit 1B2 Day 5.   Tell whether each statement is needed to show congruence. (yes or no)  The figures must have exactly the same size.  The figures.

Triangle Similarity Keystone Geometry. 2 Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding.

Warm up No, the measures are not the same Yes, angle measures are the same and the rays go to infinity No, corresponding sides are not congruent, and we.

Triangle Congruence by SSS & SAS Objective: To Determine whether triangles are congruent using SSS and SAS postulate.

Curi Yutzy ECOMP Triangle Congruence Review Use the pointer tool to draw arrows to the correct abbreviation for that congruence shortcut. Side,

Chapter 9, Section 5 Congruence. To be congruent: –corresponding parts (sides/ angles) have the same measure.

CONFIDENTIAL 1 Geometry Triangle Congruence SSS and SAS.

Objective: Prove triangle congruence using SSS and SAS.

Prove triangles congruent by ASA and AAS

4-2 Triangle Congruence by SSS and SAS

Proving Triangles Congruent

Triangle Congruence HL and AAS

Proving Triangles Congruent

Proving Triangles Congruent

Homework Questions.

Proving Triangles Congruent

Proving Triangles Congruent: SSS and SAS

Proving Triangles Congruent

Proving Triangles Congruent

4-4 and 4-5: Congruent Triangle Theorems

Proving Triangles Congruent

Proving Triangles Congruent

4-2 Some Ways to Prove Triangles Congruent (p. 122)

Similarity, Congruence, & Proofs

Triangle Congruence HL and AAS

Proving Triangles Congruent

Lucas Dougherty.

Lesson Similarity of Triangles

Similar Similar means that the corresponding sides are in proportion and the corresponding angles are congruent. (same shape, different size)

Module 1 Topic D – Lesson 24 Warm Up

Properties of Triangle Congruence

Proving Triangles Congruent

Congruent Triangles.

Objectives Apply SSS to construct triangles and solve problems.

4.2 /4.3 – Triangle Congruence

Presentation transcript:

Warm up No, the measures are not the same Yes, angle measures are the same and the rays go to infinity No, corresponding sides are not congruent, and we can’t tell if the angles are congruent. Yes, all corresponding sides are congruent and all corresponding angles are congruent. Yes, all corresponding parts are congruent. No, corresponding parts are not congruent. JM WC BA OP  L   A  J   F  M   X  P   B  K   E  N   W  O   C

4.2 Shortcuts in Triangle Congruency Remember last time… We learned that two polygons were congruent if EACH corresponding pair of angles were congruent AND each pair of corresponding sides were congruent. Remember that you had to LIST EACH PAIR? Yikes! That could get very long and tedious (boring).

Today… Today, you’re going to learn some shortcuts that apply to TRIANGLES ONLY. These shortcuts, if used correctly, will help you prove triangle congruency. Remember that congruency means EXACT size and shape… don’t confuse it with “similar”.

Side Side Side If 2 triangles have 3 corresponding pairs of sides that are congruent, then the triangles are congruent. A B C 3 inches 7 inches 5 inches X P N 3 inches 7 inches 5 inches = ~ AC PX AB PN CB XN Therefore, using SSS, ∆ABC = ∆PNX ~ = ~ = ~ = ~

Side Angle Side If two sides and the INCLUDED ANGLE in one triangle are congruent to two sides and INCLUDED ANGLE in another triangle, then the triangles are congruent. A B C 3 inches 5 inches 60° X P N 3 inches 5 inches 60° CA XP CB XN  C  X Therefore, by SAS, ∆ABC ∆PNX = ~ = ~ = ~ = ~

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, the two triangles are congruent. A B C 3 inches 60° 70° X P N 3 inches 60° 70° CA XP  A  P  C  X Therefore, by ASA, ∆ABC ∆PNX = ~ = ~ = ~ = ~

Remembering our shortcuts SSS ASA SAS (just so you know, there are 2 abbreviations that are not used for congruence: AAA and SSA)

I need 3 volunteers to hand out white boards, markers and worksheets. The worksheet is called ‘page 828’… we’ll do section 4.2 together. Let’s practice

Your Assignment Pg : 1-3, 8-19, 23-29