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Warm up

Using the quadratic formula, please solve the following equations:. Warm up. m = 2 m = -3. 2m 2 + 2m – 12 = 0 2m 2 - 7m – 13 = 0 4m 2 + 8m + 7 = 4. m = -1.35 m = 4.85. m = -.5 m = -1.5. Let’s grade your homework. Today’s Vocabulary.

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Warm up

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  1. Using the quadratic formula, please solve the following equations: Warm up 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 ab c d = abx c d y extended proportion = =

  6. means ab c d = ab c d ab c d extremes =

  7. Cross Products property ab cd = 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 AC = AT = CT GO GD OD scale 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

  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: 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.

  12. 3 = x 5 25 x = 15 x = 9 4 2 x = 18 x - 2 = 3 8 4 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 3 2 1 AC = AT = CT GO GD OD 4 = 4 = 4 YES NO 16 = 12 = 8 4 3 1 4 = 4 = 8

  14. 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. Round answers to the nearest tenth when necessary. ABCD ~ NMPO

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

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