Download 4-7 USING CORRESPONDING PARTS OF CONGRUENT

4-7 USING CORRESPONDING PARTS OF CONGRUENT TRIANGLES
(p. 224-230)
Sometimes you have to work with triangles that are overlapping. Redrawing the triangles
separately may allow you to more easily observe relationships.
Do 1a on p. 224. First, redraw the two triangles separately. Then, identify the common
side.
Do 1b on p. 224.
Example: Make a sketch where two triangles share a common angle.
In overlapping triangles, a common side or angle is congruent to itself by the familiar
reflexive property of congruence.
Example:
B
X
A
D
Y
C
Given: AX  AY, CX  AB, BY  AC
Prove: BYA  CXA, AB  AC
Plan a proof by writing a couple of sentences. Then, follow your plan and write a proof
in paragraph, flow, or two-column form.
If time, do 2 on p. 225.
In some proofs, you will need to work with more than one pair of congruent triangles. In
this case, you prove the first pair of triangles congruent so that you can use CPCTC to
prove a pair of corresponding sides or angles congruent. This congruent pair of sides or
angles will then help you prove a second pair of triangles congruent. All of this work is
done in one giant proof.
Example:
X
Y
P
W
Z
Given: XW  YZ, XWZ and YZW are right angles
Prove: XPW  YPZ
Fill in the reasons for the following proof. Use tick marks on the figure as you identify
congruent parts. You may want to redraw triangles separately.
Statements
1. XW  YZ
2. XWZ and YZW are right angles
3. XWZ  YZW
4. WZ  WZ
5. XWZ  YZW
6. WXZ  ZYW
7. XPW  YPZ
8. XPW  YPZ
Reasons
1.
2.
3.
4.
5.
6.
7.
8.
If time, do 3 on p. 225. However, 4 on p. 226 may even be better. There is no need to do
both in class. In both cases, you will need to prove two pairs of triangles congruent in the
same proof.
Homework p. 226-230: 1,3,5,8,10,11,14,18,21,24,28,30,34,35,42,48
18. Plan: First prove FDE  BDA by using vertical angles are congruent and SAS.
A  E by CPCTC. ADC  EDG by vertical angles are congruent and ASA.
21 a,b. The triangles do not have to be congruent.
24. Prove WYX  ZXY by HL.