Transcript Use ASA to Prove Triangles Congruent

Use ASA to Prove Triangles Congruent
Write a two-column proof.
Use ASA to Prove Triangles Congruent
Proof:
Statements
Reasons
1. L____
is the midpoint of 1. Given
WE.
2.
2. Midpoint Theorem
3.
3. Given
4. W  E
4. Alternate Interior Angles
5. WLR  ELD
5. Vertical Angles Theorem
6. ΔWRL  ΔEDL
6. ASA
Use AAS to Prove Triangles Congruent
Write a paragraph proof.
Apply Triangle Congruence
MANUFACTURING Barbara designs a paper
template for a certain envelope. She designs the top
and bottom flaps to be isosceles triangles that have
congruent bases and
base angles. If EV = 8 cm
and the height of the
isosceles triangle is 3 cm,
find PO.
Proving RIGHT TRIANGLES congruent
*As long as statement(s) mention right angles,
you only need 2 congruent pieces in each triangle: each hypotenuse
and corresponding legs. Hence, HL.
Example 4: Determine whether each pair of triangles is congruent.
If yes, state the postulate/theorem that applies.
4.
Each triangle has
right angles that
are congruent, a
2nd set of
corresponding
angles that are
congruent, and a
side in between
the 2 angles that is
congruent.
ASA
5.
Each triangle has
right angles that are
congruent, a 2nd set of
corresponding angles
that are congruent,
and a 3rd set of
corresponding angles
that are congruent.
NOT POSSIBLE.
(AAA does not exist)
6.
Each triangle has right
angles that are congruent, a
set of corresponding sides
that are congruent, and
share a side, but SSA does
not exist. (the angle is not
the included angle).
However, because the
triangles are right triangles,
they share the hypotenuse,
and have a set of congruent
legs. HL
Example 5: Complete the proof.
Given: AB  BC, DC  BC, AC  BD
Prove: ΔABC ΔDCB
Proof:
Statements
DCB is a right angle
ΔABC ΔDCB
Reasons
1. Given
2. Definition of 
3. Given
4. Definition of 
5. Given
6. Reflexive Property
7. HL
Five-Minute Check (over Lesson 4–4)
CCSS
Then/Now
New Vocabulary
Postulate 4.3: Angle-Side-Angle (ASA) Congruence
Example 1: Use ASA to Prove Triangles Congruent
Theorem 4.5: Angle-Angle-Side (AAS) Congruence
Example 2: Use AAS to Prove Triangles Congruent
Example 3: Real-World Example: Apply Triangle Congruence
Concept Summary: Proving Triangles Congruent
Over Lesson 4–4
Determine which postulate
can be used to prove that
the triangles are congruent.
If it is not possible to prove
congruence, choose not
possible.
A. SSS
B. ASA
C. SAS
D. not possible
Over Lesson 4–4
Determine which postulate
can be used to prove that
the triangles are congruent.
If it is not possible to prove
congruence, choose not
possible.
A. SSS
B. ASA
C. SAS
D. not possible
Over Lesson 4–4
Determine which postulate
can be used to prove that the
triangles are congruent. If it is
not possible to prove
congruence, choose not
possible.
A. SAS
B. AAS
C. SSS
D. not possible
Over Lesson 4–4
Determine which
postulate can be used to
prove that the triangles
are congruent. If it is not
possible to prove
congruence, choose not
possible.
A. SSA
B. ASA
C. SSS
D. not possible
Over Lesson 4–4
Determine which postulate
can be used to prove that
the triangles are
congruent. If it is not
possible to prove
congruence, choose not
possible.
A. AAA
B. SAS
C. SSS
D. not possible
Over Lesson 4–4
Given A  R, what sides must you know to be
congruent to prove ΔABC  ΔRST by SAS?
A.
B.
C.
D.
Content Standards
G.CO.10 Prove theorems about triangles.
G.SRT.5 Use congruence and similarity
criteria for triangles to solve problems and to
prove relationships in geometric figures.
Mathematical Practices
3 Construct viable arguments and critique
the reasoning of others.
5 Use appropriate tools strategically.
You proved triangles congruent using SSS and
SAS.
• Use the ASA Postulate to test for
congruence.
• Use the AAS Theorem to test for
congruence.
• included side