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CPCTC Proofs
Related Topics: More Lessons for Grade 9 Math Math Worksheets
Videos, worksheets, solutions, and activities to help Geometry students learn about CPCTC. CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent.
What is CPCTC? CPCTC is an acronym for corresponding parts of congruent triangles are congruent. CPCTC is commonly used at or near the end of a proof which asks the student to show that two angles or two sides are congruent. It means that once two triangles are proven to be congruent, then the three pairs of sides that correspond must be congruent and the three pairs of angles that correspond must be congruent.
How do we use CPCTC to prove corresponding parts of triangles? CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent and is used to justify two triangles are congruent in a proof. Examples:
- A and B are the endpoints of a bridge going over a river. What is the length of the bridge?
- Given YW bisects XZ. XY ≅ YZ. Prove that ∠XYW ≅ ∠ZYW.
- Given D(-5, -5), E(-3, -1), F(-2, -3), G(-2, 1), H(0, 5), and I(1, 3). Prove that ∠DEF ≅ ∠GHI.
Using CPCTC - Corresponding Parts of Congruent Triangles are Congruent Anytime you are required to prove corresponding parts of congruent triangles congruent, you will be doing a triangle proof. The two examples in this post use AAS and SAS before proving the other part of the triangle congruent using CPCTC. Examples:
- Given SL ≅ SR, ∠1 ≅ ∠2. Prove ∠3 ≅ ∠4. Now that we have proved the triangles congruent and angle 3 and angle 4 are congruent using CPCTC, what other congruence statements can you make from the diagram?
- Given ∠Q ≅ ∠R, ∠QPS ≅ ∠RSP. Prove SQ ≅ PR
SSS, SAS, ASA proofs with CPCTC Congruent triangle are triangles in which corresponding angles and sides are congruent.
Example 1: If triangle CAT ≅ triangle DOG, list all of the congruencies. How many congruencies does it take for us to show that the two triangles are congruent? How many additional congruencies could we deduce?
Example 2: Given RZ bisects ∠TRS, ∠3 ≅ ∠4. Prove ∠S ≅ ∠T
Example 3: Given AB bisects CD, ∠C ≅ ∠D. Prove ∠A ≅ ∠B
Example 4: Given M is the midpoint of AB, ∠1 ≅ ∠2, ∠3 ≅ ∠4. Prove AC ≅ BD.
How to identify and use Corresponding Parts of Congruent Figures? Learn to identify and apply the CPCTC rule Example: Use the congruent triangles below and answer the following questions. (a) What side of ABC corresponds to side YZ? (b) Name the side of triangle XYZ that corresponds to side AB. (c) What is the measure of side ZX? (d) Find the perimeter of triangle XYZ?
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Created Date: 12/4/2017 3:09:30 PM
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Day 2 - Identifying Congruent Triangles. Geometric figures are congruent if they are the same size and shape. Corresponding angles and corresponding sides are in the same _______________ in polygons with an equal number of _______.
Created Date: 2/8/2016 8:46:29 AM
How to use CPCTC, Corresponding Parts of Congruent Triangles are Congruent, SSS, SAS, ASA Proofs with CPCTC, Learn how to apply the theory of CPCTC to real world events, examples and step by step solutions, Grade 9
Find step-by-step solutions and answers to Geometry Common Core - 9780133185829, as well as thousands of textbooks so you can move forward with confidence.
CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent and is used to justify two triangles are congruent in a proof. Examples: A and B are the endpoints of a bridge going over a river. What is the length of the bridge? Given YW bisects XZ. XY ≅ YZ. Prove that ∠XYW ≅ ∠ZYW.
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 25 U1 GEOMETRY Name _____ Homework (TO BE COLLECTED) Lesson 25: CPCTC 1. If ∆()*≅∆+,-, which statement is true? (1) ∠)≅∠, (3) ()≅,- (2) ∠(≅∠- (4) (*≅+, 2.
This chapter will summarize. the key points that have been discussed throughout the book. The book is crafted in an easy-to-understand language and is complemented by engaging illustrations. This book is highly recommended for anyone seeking to gain a comprehensive understanding of Cpctc Common Core Geometry Homework.
Get instant feedback, extra help and step-by-step explanations. Boost your Geometry grade with Completing Proofs Involving Congruent Triangles and CPCTC practice problems.