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Homework Check:
P 385-387
1. Yes ∆𝐴𝐵𝐶~∆𝐹𝐸𝐷; 𝑆𝑆𝑆~𝑇ℎ𝑒𝑜𝑟𝑒𝑚
2. No,not enough information
3. Ex 1 – ratio is 2:3, Ex 2 - NA
4. Yes ∆𝐹𝐺𝐻~∆𝐾𝐽𝐻; 𝐴𝐴~𝑃𝑜𝑠𝑡𝑢𝑙𝑎𝑡𝑒
8. Yes ∆𝑁𝑀𝑃~∆𝑁𝑄𝑅; 𝑆𝐴𝑆~𝑇ℎ𝑒𝑜𝑟𝑒𝑚
9. No;
10. 𝐴𝐴~𝑃𝑜𝑠𝑡𝑢𝑙𝑎𝑡𝑒 7.5
11. 𝐴𝐴~𝑃𝑜𝑠𝑡𝑢𝑙𝑎𝑡𝑒 2.5
5
12. 𝐴𝐴~𝑃𝑜𝑠𝑡𝑢𝑙𝑎𝑡𝑒 12
6
13. 𝐴𝐴~𝑃𝑜𝑠𝑡𝑢𝑙𝑎𝑡𝑒 12
14. 𝐴𝐴~𝑃𝑜𝑠𝑡𝑢𝑙𝑎𝑡𝑒 8
17. 𝐴𝐴~𝑃𝑜𝑠𝑡𝑢𝑙𝑎𝑡𝑒 220 𝑦𝑑𝑠
19. 𝐴𝐴~𝑃𝑜𝑠𝑡𝑢𝑙𝑎𝑡𝑒 90 ft
30. 3:2
32. 12:7
34. 3:1
1. YES – 2/3=3/4.5=4/6
SSS with a ratio of 2/3
2. NO angle is not an
included angle. There are
not two pairs of sides to
compare.
Yes, ∆𝐺𝐹𝐻~𝐽𝐾𝐻 𝑏𝑦 𝐴𝐴
Yes, ∆𝑀𝑁𝑃~𝑄𝑁𝑅 𝑏𝑦 𝑆𝐴𝑆
22 30 40
≠
=
32 45 60
11 2 2
𝑁𝑜 =
≠ =
16 3 3
𝑥
4.5
10. AA
=
5
3
3𝑥 = 22.5
11. AA
5
6
=
𝑥
3
6𝑥 = 15
𝑥 = 2.5
𝑥 = 7.5
12. AA
13. AA
6
9
=
8
𝑥
=
𝑥
22
24𝑥 = 308
𝑥 = 12.83
6𝑥 = 72
𝑥 = 12
14
24
14. AA
5
15
=
4
4+𝑥
60 = 5(4 + 𝑥)
60 = 20 + 5𝑥
40 = 5𝑥
𝑥=8
𝐴𝐴
110
𝑥
=
90
180
𝑥 = 220 𝑦𝑎𝑟𝑑𝑠
𝐴𝐴
120
𝑥
=
20
15
𝑥 = 90 𝑓𝑡
24: 14 𝑜𝑟 12: 7
4.5: 3 𝑜𝑟 3: 2
15: 5 𝑜𝑟 3: 1
Make a list on a notecard of perfect
squares up through 30.
Algebra Review: Simplifying Radicals
A radical expression is simplified when:
The number under the radical sign has no factors that are perfect squares other than 1.
The number under the radical does not contain a fraction.
There is no radical expression in the denominator
You can multiply and divide numbers that are under a radical sign.
2∙ 8
Rewrite using one radical sign
Simplify the expression under the radical.
Factor out perfect squares and simplify.
2∙ 8= 2∙8
= 16
=4
294 ÷ 3
294 ÷ 3 = 294 ÷ 3
= 98
= 49 ∙ 2
=7 2
Simplifying a fraction under a radical:
4
3
Rewrite as the quotient of two radicals.
Simplify.
Multiply by a well-chosen “1” rationalize the denominator.
Simplify
4
4
=
3
3
2
=
3
=
2
=
3
∙
2 3
3
3
3
Write in simplest form:
5 ∙ 10
1.
2.
3.
4.
243
8
28
6∙
3
9
ANSWERS:
1.
2.
3.
4.
5 ∙ 10
1.
5 2
243
2.
9 3
3.
14
7
8
28
6∙
3
9
4.
2