Congruence

CONGRUENT ANGLES

1. m∠3 = 4x − 11 and m∠1 = 5x + 2. Find m∠2.

2. Find the values of x and y.

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3. Find the value of x and y.

4. CD is an angle bisector of the triangle and CD ⊥ AB. m∠CAD = 5x − 10

and m∠BCD = 25. Find x.

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TRIANGLE CONGRUENCE WITH SSS, ASA, SAS

1. Fill in the blank. △ ABC ≅ △ ADC by the ______________ Theorem.

2. Fill in the blank. L is a midpoint of JN. △ JKL ≅ △ NML by the

______________ Theorem.

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3. △ PRQ ≅ △ ______________ by the ______________ Theorem.

4. △ PMD is an isosceles triangle with vertex angle at M. N is a midpoint

of PD. △ PMN ≅ △ DMN by the ______________ Theorem.

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TRIANGLE CONGRUENCE WITH AAS, HL

1. Which theorem could be used to prove △ PRS ≅ △ XTS?

2. Which theorem could be used to prove △ ACB ≅ △ ECD? The

following facts are given about the triangles.

AE ⊥ BC, AB ≅ DC, and C is a midpoint of AE

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3. What additional information would we need to prove these triangles

are congruent using AAS Theorem?

4. ABCD is a rectangle. BEC is an isosceles triangle with vertex angle at E.

Write a proof to verify that △ BAE ≅ △ CDE by the HL Theorem.

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ISOSCELES TRIANGLE THEOREM

1. Find the values of x and y.

2. △ JKL is isosceles with vertex angle K. JK = 4x − 5, LK = 3x + 8, and

m∠J = 2x + 4. Find m∠L.

3. Find m∠ABC.

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4. Find x.

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CPCTC

1. Fill in the blank. Given △ LMO ≅ △ SQR, LO ≅ ______________.

2. Determine whether ∠M ≅ ∠N. Justify your answer.

3. △ DOG ≅ △ TCA by SSS. What three conclusions can be drawn by

CPCTC?

4. Given ∠1 ≅ ∠3 and ∠2 ≅ ∠4, prove AB ≅ CD.

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5. Given that L is the midpoint of JN and KM, prove JK ≅ NM.

6. Given that △ CAB is an isosceles triangle, that D is the midpoint of CE,

and that E is the midpoint of BD, prove that △ DAE is isosceles.

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