Exploring Congruent Triangles
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Transcript of Exploring Congruent Triangles
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Section 4.5
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Warm Up
1. Name all sides and angles of ∆FGH.
2. What is true about K and L? Why?
3. What does it mean for two segments to be congruent?
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Two geometric figures with exactly the same size and shape.
The Idea of a CongruenceThe Idea of a Congruence
A C
B
DE
F
Each triangle is made up of six parts:3 sides and 3 angles
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If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.
Corresponding PartsCorresponding Parts
ABC DEF
B
A C
E
D
F
1. AB DE
2. BC EF
3. AC DF
4. A D
5. B E
6. C F
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CPCTCCorresponding Parts of Congruent Triangles are Congruent.
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Congruency amongst triangles does not change when you…
slide (translation),
Turn (rotation),
or flip (reflection) … the triangles.
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EXAMPLE 1 Identify congruent parts
Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts.
SOLUTION
The diagram indicates that JKL TSR.
Corresponding sides JK TS KL SR LJ RT
Corresponding angles J T, K S, L R
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Complete each congruence statement.
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Write a congruence statement.
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Given ΔBCD = ΔRST, m C = 57, m R = 64, m D = 5x + 4. Find x and m T.
Given ΔQRS = ΔLMN, RS = 8, QR=14, QS=10, MN = 3x – 25. Find x.
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Name the corresponding angles and sides if ΔBCD = ΔEFG.
Given ΔCAT = ΔDOG, CA=14, AT=18, TC=21 and DG=2x+7, find the value of x.
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Given: ∆ABC ∆DBC. Find the value of x and mDBC.
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Given: ∆ABC ∆DEFFind the value of x.
Find mF.
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Lesson Quiz
1. ∆ABC ∆JKL and AB = 2x + 12. JK = 4x – 50. Find x and AB.
Given that polygon MNOP polygon QRST, identify the congruent corresponding part.
2. NO ____ 3. T ____