2. Essential Questions
How do you use the SSS Postulate to test for triangle
congruence?
How do you use the SAS Postulate to test for triangle
congruence?
4. Vocabulary
1. Included Angle: An angle formed by two adjacent sides of a
polygon
Postulate 4.1 - Side-Side-Side (SSS) Congruence:
Postulate 4.2 - Side-Angle-Side (SAS) Congruence:
5. Vocabulary
1. Included Angle: An angle formed by two adjacent sides of a
polygon
Postulate 4.1 - Side-Side-Side (SSS) Congruence: If three sides
of one triangle are congruent to three corresponding sides of
a second, then the triangles are congruent
Postulate 4.2 - Side-Angle-Side (SAS) Congruence:
6. Vocabulary
1. Included Angle: An angle formed by two adjacent sides of a
polygon
Postulate 4.1 - Side-Side-Side (SSS) Congruence: If three sides
of one triangle are congruent to three corresponding sides of
a second, then the triangles are congruent
Postulate 4.2 - Side-Angle-Side (SAS) Congruence: If two sides
and the included angle of one triangle are congruent to two
corresponding sides and included angle of a second triangle,
then the triangles are congruent
7. Example 1
Prove the following.
Given: QU â AD, QD â AU
Prove: âłQUD â âłADU
8. Example 1
Prove the following.
Given: QU â AD, QD â AU
Prove: âłQUD â âłADU
1. QU â AD, QD â AU
9. Example 1
Prove the following.
Given: QU â AD, QD â AU
Prove: âłQUD â âłADU
1. QU â AD, QD â AU 1. Given
10. Example 1
Prove the following.
Given: QU â AD, QD â AU
Prove: âłQUD â âłADU
1. QU â AD, QD â AU 1. Given
2. DU â DU
11. Example 1
Prove the following.
Given: QU â AD, QD â AU
Prove: âłQUD â âłADU
1. QU â AD, QD â AU 1. Given
2. DU â DU 2. ReïŹexive
12. Example 1
Prove the following.
Given: QU â AD, QD â AU
Prove: âłQUD â âłADU
1. QU â AD, QD â AU 1. Given
2. DU â DU 2. ReïŹexive
3. DU â UD
13. Example 1
Prove the following.
Given: QU â AD, QD â AU
Prove: âłQUD â âłADU
1. QU â AD, QD â AU 1. Given
2. DU â DU 2. ReïŹexive
3. DU â UD 3. Symmetric
14. Example 1
Prove the following.
Given: QU â AD, QD â AU
Prove: âłQUD â âłADU
1. QU â AD, QD â AU 1. Given
2. DU â DU 2. ReïŹexive
3. DU â UD 3. Symmetric
4. âłQUD â âłADU
15. Example 1
Prove the following.
Given: QU â AD, QD â AU
Prove: âłQUD â âłADU
1. QU â AD, QD â AU 1. Given
2. DU â DU 2. ReïŹexive
3. DU â UD 3. Symmetric
4. âłQUD â âłADU 4. SSS
16. Example 2
âDVW has vertices D(â5, â1), V(â1, â2), and W(â7, â4). âLPM
has vertices L(1, â5), P(2, â1), and M(4, â7). Graph both
triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not,
providing a logical argument for your statement.
17. Example 2
âDVW has vertices D(â5, â1), V(â1, â2), and W(â7, â4). âLPM
has vertices L(1, â5), P(2, â1), and M(4, â7). Graph both
triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not,
providing a logical argument for your statement.
x
y
18. Example 2
âDVW has vertices D(â5, â1), V(â1, â2), and W(â7, â4). âLPM
has vertices L(1, â5), P(2, â1), and M(4, â7). Graph both
triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not,
providing a logical argument for your statement.
x
y
D
19. Example 2
âDVW has vertices D(â5, â1), V(â1, â2), and W(â7, â4). âLPM
has vertices L(1, â5), P(2, â1), and M(4, â7). Graph both
triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not,
providing a logical argument for your statement.
x
y
D
V
20. Example 2
âDVW has vertices D(â5, â1), V(â1, â2), and W(â7, â4). âLPM
has vertices L(1, â5), P(2, â1), and M(4, â7). Graph both
triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not,
providing a logical argument for your statement.
x
y
D
V
W
21. Example 2
âDVW has vertices D(â5, â1), V(â1, â2), and W(â7, â4). âLPM
has vertices L(1, â5), P(2, â1), and M(4, â7). Graph both
triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not,
providing a logical argument for your statement.
x
y
D
V
W
22. Example 2
âDVW has vertices D(â5, â1), V(â1, â2), and W(â7, â4). âLPM
has vertices L(1, â5), P(2, â1), and M(4, â7). Graph both
triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not,
providing a logical argument for your statement.
x
y
D
V
W
L
23. Example 2
âDVW has vertices D(â5, â1), V(â1, â2), and W(â7, â4). âLPM
has vertices L(1, â5), P(2, â1), and M(4, â7). Graph both
triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not,
providing a logical argument for your statement.
x
y
D
V
W
L
P
24. Example 2
âDVW has vertices D(â5, â1), V(â1, â2), and W(â7, â4). âLPM
has vertices L(1, â5), P(2, â1), and M(4, â7). Graph both
triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not,
providing a logical argument for your statement.
x
y
D
V
W
L
P
M
25. Example 2
âDVW has vertices D(â5, â1), V(â1, â2), and W(â7, â4). âLPM
has vertices L(1, â5), P(2, â1), and M(4, â7). Graph both
triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not,
providing a logical argument for your statement.
x
y
D
V
W
L
P
M
26. Example 2
âDVW has vertices D(â5, â1), V(â1, â2), and W(â7, â4). âLPM
has vertices L(1, â5), P(2, â1), and M(4, â7). Graph both
triangles on the coordinate plane. Then, using your drawing,
determine whether the triangles are congruent or not,
providing a logical argument for your statement.
x
y
D
V
W
L
P
M
These are congruent. What
possible ways could we show this?
27. Example 3
Prove the following.
Prove: âłFEG â âłHIG
Given: EI â FH, G is the midpoint of EI and FH
28. Example 3
Prove the following.
Prove: âłFEG â âłHIG
Given: EI â FH, G is the midpoint of EI and FH
1. EI â FH, G is the midpoint of EI and FH
29. Example 3
Prove the following.
Prove: âłFEG â âłHIG
Given: EI â FH, G is the midpoint of EI and FH
1. EI â FH, G is the midpoint of EI and FH 1. Given
30. Example 3
Prove the following.
Prove: âłFEG â âłHIG
Given: EI â FH, G is the midpoint of EI and FH
1. EI â FH, G is the midpoint of EI and FH 1. Given
FG â HG, EG â IG2.
31. Example 3
Prove the following.
Prove: âłFEG â âłHIG
Given: EI â FH, G is the midpoint of EI and FH
1. EI â FH, G is the midpoint of EI and FH 1. Given
FG â HG, EG â IG2. 2. Midpoint Thm.
32. Example 3
Prove the following.
Prove: âłFEG â âłHIG
Given: EI â FH, G is the midpoint of EI and FH
1. EI â FH, G is the midpoint of EI and FH 1. Given
FG â HG, EG â IG2. 2. Midpoint Thm.
â FGE â â HGI3.
33. Example 3
Prove the following.
Prove: âłFEG â âłHIG
Given: EI â FH, G is the midpoint of EI and FH
1. EI â FH, G is the midpoint of EI and FH 1. Given
FG â HG, EG â IG2. 2. Midpoint Thm.
â FGE â â HGI3. 3. Vertical Angles Thm.
34. Example 3
Prove the following.
Prove: âłFEG â âłHIG
Given: EI â FH, G is the midpoint of EI and FH
1. EI â FH, G is the midpoint of EI and FH 1. Given
FG â HG, EG â IG2. 2. Midpoint Thm.
â FGE â â HGI3. 3. Vertical Angles Thm.
4. âłFEG â âłHIG
35. Example 3
Prove the following.
Prove: âłFEG â âłHIG
Given: EI â FH, G is the midpoint of EI and FH
1. EI â FH, G is the midpoint of EI and FH 1. Given
FG â HG, EG â IG2. 2. Midpoint Thm.
â FGE â â HGI3. 3. Vertical Angles Thm.
4. âłFEG â âłHIG 4. SAS