View
251
Download
5
Category
Tags:
Preview:
Citation preview
4-5 Proving Triangles Congruent – ASA, AAS
You proved triangles congruent using SSS and SAS.
• Use the ASA Postulate to test for congruence.
Angle-Side-Angle Congruence Postulate (ASA)
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Page 275
Use ASA to Prove Triangles Congruent
4. Alternate Interior Angles4. W E
Statements Reasons
1. Given1. L is the midpoint of WE.____
3. Given3.
2. Midpoint Theorem2.
5. Vertical Angles Theorem5. WLR ELD
6. ASA6. ΔWRL ΔEDL
A. SSS B. SAS
C. ASA D. AAS
Fill in the blank in the following paragraph proof.
Side-Angle-Side Congruence Postulate (SAA)
If two angles and a side opposite one of them in one triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent.
Try It
If possible, what is the congruence statement for this pair of triangles? If the triangles are not congruent, say so.
A
B
C
M
NO
Needs more information
Try It
If possible, what is the congruence statement for this pair of triangles? If the triangles are not congruent, say so.
SAA;RQPDEF
R
D
E F
20°
130°
P Q
20°
130°
Write a paragraph proof.
Proof: NKL NJM, KL MN, and N N by the Reflexive property. Therefore, ΔJNM ΔKNL by AAS. By CPCTC, LN MN.
__ ___
_____
A. SSS B. SAS
C. ASA D. AAS
Complete the following flow proof.
A. SSS
B. SAS
C. ASA
D. AAS
The curtain decorating the window forms 2 triangles at the top. B is the midpoint of AC. AE = 13 inches and CD = 13 inches. BE and BD each use the same amount of material, 17 inches. Which method would you use to prove ΔABE ΔCBD?
Page 278
What are the four short cuts to prove triangles congruent?
• Side-Side-Side (SSS)• Side-Angle-Side (SAS)• Angle-Side-Angle (ASA)• Side-Angle-Angle (SAA)
4-5 Assignment
Page 278, 1, 4, 9, 10• Write as a two column proof.• Write out Given and Prove.• Draw the figure.
Recommended