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Similar vs. Congruent. 5-3. Yes No No Yes No Yes No Yes Yes No No No Not proportional Proportional Proportional Not proportional Proportional Not proportional Not proportional Proportional Proportional Not proportional Proportional Proportional No yes. 5-4. 8 14 - PowerPoint PPT Presentation
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Similar vs. Congruent
5-31. Yes
2. No
3. No
4. Yes
5. No
6. Yes
7. No
8. Yes
9. Yes
10. No
11. No
12. No
13. Not proportional
14. Proportional
15. Proportional
16. Not proportional
17. Proportional
18. Not proportional
19. Not proportional
20. Proportional
21. Proportional
22. Not proportional
23. Proportional
24. Proportional
25. No
26. yes
5-41. 8
2. 14
3. 15
4. 7.5
5. 28
6. 6
7. 35
8. 20
9. 9
10. 6
11. 2
12. 18
13. $12,000
14. 1c
15. 67.5 min
16. 364 mi
17. 60 days
18. 18 eggs
Similar or Congruent?
Similar or Congruent?
Similar or Congruent?
Congruent or Similar?
EXITBACK NEXT
How do we know if two triangles are
similar or proportional?
EXITBACK NEXT
Triangles are similar (~) if corresponding angles are equal and the ratios of the lengths of corresponding sides are equal.
A
B
C
The sum of the measure of the angles of a triangle is 1800.
Ð A + Ð B + ÐC =1800
Interior Angles of Triangles
Determine whether the pair of triangles is similar. Justify your answer.
Answer: Since the corresponding angles have equal measures, the triangles are similar.
AB =KXY
BC =KYZ
AC =KXZ
2612
= 248= 2
510
=
This tells us that ABC and XYZ are similar and proportional.
Q: Can these triangles be similar?
Answer—Yes, right triangles can also be similar but use the criteria.
AB =XY
BC =YZ
AC = KXZ
6 8 10 = = = K4 6 8
AB =XY
BC =YZ
AC = KXZ
6 8 10 = = = K4 6 8
6 8 = 1.5 but = 1.3 4 6
This tells us our triangles are not similar. You can’t have two different scaling factors!
Do we have equality?
If we are given that two triangles are similar or proportional what can we determine about the triangles?
The two triangles below are known to be similar, determine the missing value X.
x5.4
55.7=
x5.4
55.7=
x5.75.45 =
x5.75.22 =
x=3
A
B
C
P
Q
R10
6
c
5
4 d
In the figure, the two triangles are similar. What are c and d ?
4510 c
= c540= c=8
A
B
C
P
Q
R10
6
c
5
4 d
In the figure, the two triangles are similar. What are c and d ?
d6
510
= d1030= d=3
Sometimes we need to measure a distance indirectly. A common method of indirect measurement is the use of similar triangles.
h
6
17102
h6
10217
=
h=36
