Applying Congruence Congruent Figures Two figuresshapes are congruent

Warm-Up 1 Exercises EXAMPLE Identify congruent parts Write a congruence statement for the triangles.

Warm-Up 2 Exercises EXAMPLE Use properties of congruent figures In the diagram, DEFG SPQR.

Warm-Up 2 Exercises EXAMPLE Use properties of congruent figures b. You know that ∠F

Warm-Up 3 Exercises EXAMPLE Show that figures are congruent PAINTING If you divide the

Warm-Up 3 Exercises EXAMPLE Show that figures are congruent Then, 1 4 and 2

Warm-Up Exercises GUIDED PRACTICE for Examples 1, 2, and 3 In the diagram at

Warm-Up 4 Exercises EXAMPLE Use the Third Angles Theorem Find m BDC. SOLUTION A

Warm-Up Exercises GUIDED PRACTICE for Examples 4 and 5 4. In the diagram, what

Daily Homework Quiz Warm-Up Exercises In the diagram, 1. m A= ? ANSWER 2.

Daily Homework Quiz Warm-Up Exercises 4. Write a congruence statement for the two small

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Applying Congruence Congruent Figures: Two figures/shapes are congruent iff the corresponding angles and sides are congruent. Same size and same shape. Transformations can be used to show that two shapes are congruent.

Warm-Up 1 Exercises EXAMPLE Identify congruent parts Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts. SOLUTION The diagram indicates that Corresponding angles J Corresponding sides JK JKL T, ∠ K TS, KL TSR. S, SR, LJ L R RT

State all of the congruent parts.

Warm-Up 2 Exercises EXAMPLE Use properties of congruent figures In the diagram, DEFG SPQR. a. Find the value of x. b. Find the value of y. SOLUTION a. You know that FG FG = QR 12 = 2 x – 4 16 = 2 x 8=x QR.

Warm-Up 2 Exercises EXAMPLE Use properties of congruent figures b. You know that ∠F m F=m Q 68 o = (6 y + x) 68 = 6 y + 8 10 = y Q. o

Warm-Up 3 Exercises EXAMPLE Show that figures are congruent PAINTING If you divide the wall into orange and blue sections along JK , will the sections of the wall be the same size and shape? Explain. SOLUTION From the diagram, A C and D B because all right angles are congruent. Also, by the Lines Perpendicular to a Transversal Theorem, AB DC.

Warm-Up 3 Exercises EXAMPLE Show that figures are congruent Then, 1 4 and 2 3 by the Alternate Interior Angles Theorem. So, all pairs of corresponding angles are congruent. The diagram shows AJ CK , KD JB , and DA BC. By the Reflexive Property, JK KJ. All corresponding parts are congruent, so AJKD CKJB.

Warm-Up Exercises GUIDED PRACTICE for Examples 1, 2, and 3 In the diagram at the right, ABGH CDEF. 1. Identify all pairs of congruent corresponding parts. SOLUTION Corresponding sides: Corresponding angles: AB CD, BG DE, GH FE, HA FC A G C, B E, H D, F.

Warm-Up Exercises GUIDED PRACTICE for Examples 1, 2, and 3 In the diagram at the right, ABGH 2. Find the value of x and find m SOLUTION (a) You know that (4 x+ 5)° = 105° 4 x = 100 x = 25 (b) You know that H m F =105° H F F CDEF. H.

Warm-Up 4 Exercises EXAMPLE Use the Third Angles Theorem Find m BDC. SOLUTION A B and ADC BCD, so by the Third Angles Theorem, ACD BDC. By the Triangle Sum Theorem, m ACD = 180° – 45° – 30° = 105°. ANSWER So, m ACD = m BDC = 105° by the definition of congruent angles.

Warm-Up Exercises GUIDED PRACTICE for Examples 4 and 5 4. In the diagram, what is m DCN. SOLUTION CDN NSR, DNC SNR then the third angles are also congruent NRS DCN = 75°

Daily Homework Quiz Warm-Up Exercises In the diagram, 1. m A= ? ANSWER 2. FD 60° ? ANSWER 3. EDF ANSWER ABC CA ? BAC DEF. Complete the statement.

Daily Homework Quiz Warm-Up Exercises 4. Write a congruence statement for the two small triangles. Explain your reasoning. ANSWER WXZ YXZ; The diagram tell us that W Y and WZX YZX. WXZ YXZ by the Third s Thm. From the diagram WX YX and WZ YZ, and XZ XZ by Refl. Prop. Of Segs.