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

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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.

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

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

means a b c d = a b c d a b c d extremes =

Cross Products property a b c d = ad = bc

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.

similar figures similar polygons

scale drawing scale factor scale AC = AT = CT GO GD OD 16 = 12 = 8 16 = 12 = 8 4 3 2 4 = 4 = 4 Every 1 mm on this drawing, corresponds to 10 mm on the real horse. The scale factor is 4

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: 2900 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.

3 = x 5 25 x = 15 x = 9 4 2 x = 18 x - 2 = 3 8 4 x = 8

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 3 2 4 = 4 = 4 4 = 4 = 8 AC = AT = CT GO GD OD 16 = 12 = 8 4 3 1 1 YES NO

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:

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

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

Your assignment 7-1 and 7-2 Practice worksheets