Download Unit 4: Triangle Congruence

Unit 4: Triangle Congruence
4.5 Triangle Congruence: ASA
4.5 Triangle Congruence: ASA
Warm Up 12/01/11 (HW #23 [4.5] Pgs 257 - 258 #s 11, 12, 14 – 17, 22)
1. Show that ∆ADB  ∆CDB, t = 4.
4.5 Triangle Congruence: ASA
Warm Up 12/01/11 (HW #23 [4.5] Pgs 257 - 258 #s 11, 12, 14 – 17, 22)
1.
What are sides AC and BC called? Side AB?
2. Which side is in between A and C?
3. Given DEF and GHI, if D  G and E  H, why is
F  I?
Objectives
(see page 252)
Apply ASA to construct triangles and to solve
problems.
Prove triangles congruent by using ASA.
*Standard 5.0 Students prove that triangles are
congruent or similar, and they are able to use the
concept of corresponding parts of congruent triangles.
*also Standard 4.0 Students prove basic theorems
involving congruence and similarity.
*also Standard 2.0 Students write geometric proofs,
including proofs by contradiction.
*see page 252
An included side is the common side of two
consecutive angles in a polygon. The
following postulate uses the idea of an
included side.
Your Goal! Discuss and Decide if you can…
create 2 triangles that are exactly the same
Your task (how you will accomplish your goal)!
1. Find your partner who has the same size and color
marked bamboo stick OR angle as you
2. With your partner, form a group of 6 (you should
have 2 bamboo sticks and 4 angles)
3. Within your group of 6, can you form 2 triangles that
are the same using 2 angles and an included side
(bamboo stick) for each? (on the paper provided, write
your response and a figure or words to describe how you
know)
Your Goal! Discuss and Decide if you can…
create 2 triangles that are exactly the same
Your task (continued)!
4. Now that you’ve discussed and decided that each
group has 2 exactly the same triangles… set aside
one triangle and focus on the other triangle.
Keeping the 2 angles with the included side
together, can you rearrange the triangle to make it
different from the triangle you set aside?
*see page 252
Example 2: Applying ASA Congruence
page 253)
(see example 2 on
Determine if you can use ASA to prove the triangles
congruent. Explain.
Check It Out! Example 2 (see page 253)
Determine if you can use ASA to
prove NKL  LMN. Explain.
Given: FAB  GED,
ABC   DCE, AC  EC
Prove: ABC  EDC
Statements
Reasons
1. FAB  GED
1.
2. BAC is a supp. of FAB;
DEC is a supp. of GED.
2. Def. of supp. s
3. BAC  DEC
3.  Supp. Thm.
4. ACB  DCE; AC  EC
4.
5. ABC  EDC
5.