EXAMPLE 1 Identify congruent parts

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Presentation transcript:

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 angles J T, ∠ K S, L R Corresponding sides JK TS, KL SR, LJ RT

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

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

EXAMPLE 3 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 .

EXAMPLE 3 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.

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

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

GUIDED PRACTICE for Examples 1, 2, and 3 In the diagram at the right, ABGH CDEF. 3. Show that PTS RTQ. SOLUTION In the given diagram PS QR, PT TR, ST TQ and Similarly all angles are to each other, therefore all of the corresponding points of PTS are congruent to those of RTQ by the indicated markings, the Vertical Angle Theorem and the Alternate Interior Angle theorem.