1. 5.2 Congruent Polygons

2. Identifying and Using Corresponding Parts
A rigid motion maps each part of a figure to a corresponding part of its image. Because rigid motions preserve length and angle measure, corresponding parts of congruent figures are congruent.
When ∆DEF is an image of ∆ABC after a rigid motion or a composition of rigid motions, you can write congruence statements for the corresponding angles and corresponding sides.

3. When you write a congruence statement for two polygons, always list the corresponding vertices in the same order.
Possible congruence statement for the above triangles could be:
∆ABC = ∆DEF
∆BCA = ∆EFD

4. Example 1: Identifying Corresponding Parts
Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts.

5. Example 2: Using Properties of Congruent Figures
In the diagram, DEFG = SPQR.
Find x.
We know that FG= QR.
12 = 2x – 4
16 = 2x
8 = x

6. Example 2: Using Properties of Congruent Figures
In the diagram, DEFG = SPQR.
b) Find y.
We know that m<F = m<Q.
68 = 6y + x
68 = 6y + 8
60 = 6y
10 = y

7. Example 3: Showing that Figures are Congruent
You divide a wall into orange and blue sections along segment JK. Will the sections of the wall be the same shape and size? Explain.
From the diagram, <A = <C and <D = <B, since all right triangles are congruent. By the Lines Perpendicular to a Transversal Theorem, segment AB is parallel to segment DC. <1 = <4 and <2 = <3 because of Alternate Interior Angles Theorem. So, all pairs of corresponding angles are congruent.
The diagram shows AJ = CK, DK = BJ and AD = CB. By the Reflexive Property of Congruency JK = KJ. So, all pairs of corresponding sides are congruent.
Because all corresponding parts are congruent, AJKD = CKJB.

8. You try! In the diagram ABGH = CDEF.
Identify all pairs of congruent corresponding parts.
2) Find the value of x.
<A = <C
<B = <D
<H = <F
<G = <E
AB = CD
AH = CF
HG = FE
GB = ED
4x + 5 = 105
4x = 100
x = 25

9. You try! 3) In the diagram, show that ∆PTS = ∆RTQ.
Since segment PS is parallel to segment RQ, <P= <R because of Alternate Interior Angles Theorem(transversal being PR) and <S = <Q because of Alternate Interior Angles Theorem (transversal being SQ). <T = <T because of Reflexive Property of Congruence.
The diagram shows that each side is congruent to its corresponding side. So, since all corresponding parts are congruent ∆PTS = ∆RTQ.

11. Example 4: Using the Third Angles Theorem
Find m<BDC.

12. Example 5: Proving that Triangles are Congruent
Complete on whiteboard.