Download Chapter 4 Congruent Triangles

Chapter 4 Congruent Triangles
4-1 Congruent Figures
Objectives
Students will be able to:
Recognize congruent figures and their corresponding
parts
Define and apply the third angles theorem
Use congruent parts to prove triangles congruent
Essential Understanding
You can determine whether two figures are congruent
by comparing their corresponding parts.
Congruent Figures
What do you know about congruent figures?
Does the orientation of congruent figures matter?
No, the congruent figures can be slid, flipped, or
turned and they will still be congruent
Congruent Figures
Congruent Polygons:
Have congruent corresponding parts
(equal sides and angles)
When naming congruent figures, you must list corresponding
parts (angles/vertices) in the same order
Corresponding Parts
If figure HIJK ≅ LMNO, what are the congruent corresponding
parts?
If it helps, draw a picture
Then name the corresponding segments
HI ≅ LM
IJ ≅ MN JK ≅ NO KH ≅ OL
Then name the corresponding angles
<H ≅ <L <I ≅ <M <J ≅ <N <K ≅ <O
If ΔABC ≅ ΔXYZ, what are the congruent corresponding parts?
Congruent Parts
Suppose ΔABC ≅ ΔFED, <B = 30 and <D = 75, what is
the measure of <A?
Draw a picture of the situation
Suppose ΔWYS ≅ ΔMKV. If <W = 62 and <Y = 35,
what is the measure of <V? How do you know?
Third Angles Theorem
If you know two angles of a triangle are congruent, then the
third angles will be congruent.
Are the triangles
congruent?
Write a two column proof
To prove two triangle congruent you need to get all the
corresponding angles and segments to be congruent. This allows
you to use the Def. of Congruent Triangles reason as your final
statement
Statements
|
Reasons
.
1. AB ≅ AD, BC ≅ DC,
<B ≅ <D
1. Given
2. AC ≅ AC
2. Reflexive Property of ≅
3.<BCA ≅ <DCA
3. All right angles are congruent
4. <BAC ≅ <DAC
5. ΔABC ≅ ΔADC
4. Third <s Thm.
5. Def of Congruent Triangles
Are the Triangles Congruent?
No because we cannot show that all the corresponding
parts are congruent.
Proving Triangles Congruent
Given: <A ≅ <D, AE ≅ DC, EB ≅ CB, BA ≅ BD
Prove: ΔAEB ≅ ΔDCB
Homework
Pg. 222 -223
10 – 19, 30 – 32, 44
14 problems