1. Using the quadratic formula, please solve the following equations:
Warm up
Using the quadratic formula, please solve the following equations:
m = 2
m = -3
2m2 + 2m – 12 = 0
2m2 - 7m – 13 = 0
4m2 + 8m + 7 = 4
m = -1.35
m = 4.85
m = -.5
m = -1.5

2. Let’s grade your homework

3. Today’s Vocabulary Ratio – a comparison of two things – a/b….. a:b
Extended ratio – a comparison of three or more things – a:b:c
Proportion – two ratios set equal to each other – a/b = c/d
Extended proportion – three or more ratios set equal to each other: a/b = c/d = m/n = x/y
Extremes – the first and last terms in a proportion A/b = c/D
A and D are the extremes
Means – the middle terms in a proportion a/B = C/d B and C are the means
Cross Products Property – multiplying the means and extremes to solve an equation. Remember you can only do this when you have a proportion.

4. ratio a c
or a:c
extended ratio
a:c:x:y

5. proportion
a b
c d =
a b x
c d y
extended
proportion = =

6. means
a b
c d =
a b
c d
a b
c d
extremes =

7. Cross Products
property
a b
c d =
ad = bc

8. more of Today’s Vocabulary
Similar figures – things that have the same shape but are generally a different size.
Similar polygons – polygons that have the same shape but are a different size
Scale - a ratio that compares each length in a scale drawing.
Scale factor - The ratio of corresponding linear measurements of two similar figures.
Scale drawing - A drawing where all lengths are proportional to their corresponding actual lengths.

9. similar figures
similar polygons

10. scale drawing scale factor scale AC = AT = CT GO GD OD 16 = 12 = 8
16 = 12 = 8
4 = 4 = 4
Every 1 mm on this drawing, corresponds to 10 mm on the real horse.
The scale factor is 4

11. let’s brush up and practice
Write the ratio of the first measurement to the second measurement.
Convert to inches: (14)(12) + 10 = 178
length of car: 14 ft 10 in.
length of model car: 8 in
178 : 8
2900: .5
weight of car: lb
weight of model car: 8 oz
convert : 8 oz = ½ lb = .5 lb
3. There are 238 juniors at Torrington High School. The ratio of girls to boys in the junior class is 3:4. How many juniors are girls? How many are boys?
3x + 4x = 238
x = 34
There are 102 girls and 136 boys in the junior class.

12. 3 = x
x = 15
x = 9
x = 18
x - 2 = 3
x = 8

13. Similar polygons have corresponding angles that are congruent and corresponding sides that are proportional.
An extended proportion can be written for the ratios of corresponding sides of similar polygons.
AC = AT = CT
GO GD OD
16 = 12 = 8
4 = 4 = 4
4 = 4 = 8
AC = AT = CT
GO GD OD
16 = 12 = 8 1
YES NO

14. Let’s see if these quadrilaterals are similar
Let’s see if these quadrilaterals are similar. If they are, we’ll need to write a similarity statement and an extended proportion.
Compare angles: A  X, B  Y.
C  Z, D  W
Compare ratios of sides:
Because corresponding sides are proportional and corresponding angles are congruent,
ABCD ~ XYZW.
The extended proportion for the ratios of corresponding sides is:

15. Are these triangles similar?
Let’s check the congruency of angles and the proportionality of the sides.

16. Give the scale factor of the polygons. Find the value of x
Give the scale factor of the polygons. Find the value of x. Round answers to the nearest tenth when necessary.
ABCD ~ NMPO

17. Your assignment
7-1 and 7-2 Practice worksheets