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4.2 Apply  to Δ ’ s. OBJECTIVES. Name and label corresponding parts of congruent triangles.  Δ ’ s. Triangles ( actually, ALL geometric figures) that are the same shape and size are congruent. Each triangle has three sides and three angles.

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4.2 Apply to Δ’s

• Name and label corresponding parts of congruent triangles

Δ’s

• Triangles (actually, ALL geometric figures) that are the same shape and size are congruent.

• Each triangle has three sides and three angles.

• If all six of the corresponding parts are congruent then the triangles are congruent.

• CPCTC

Corresponding Parts of Congruent Triangles are Congruent

• Be sure to label Δs with proper mappings(i.e. if D  L, V  P, W  M, DV  LP, VW  PM, and WD  ML, then we must write ΔDVW ΔLPM)

Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts.

The diagram indicates that

JKL TSR.

Corresponding angles

J T, K S, L R

Corresponding sides

JK TS KL SR LJ RT

EXAMPLE 1

Identify Congruent Parts

SOLUTION

In the diagram, pairs of congruent corresponding parts.DEFG SPQR.

Find the value of x.

Find the value of y.

You know that FG QR.

FG

= QR

= 2x – 4

12

16

= 2x

8

= x

EXAMPLE 2

EXAMPLE 2

Use Properties of Congruent Figures

SOLUTION

You know that pairs of congruent corresponding parts.∠ F Q.

m F

= mQ

68

= 6y + 8

68

= (6y + x)

10

= y

EXAMPLE 2 (continued)

EXAMPLE 2

Use Properties of Congruent Figures

Theorem 4.3 – Third Angles Theorem pairs of congruent corresponding parts.

If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangle are congruent.

Abbreviation: If 2 s of one Δ are  to 2 s of another Δ, then third s are .

ASSIGNMENT pairs of congruent corresponding parts.

• Pre-AP Geometry: Pgs. 228 - 231 #4 – 21, 26