Lesson 1

Scale Drawings

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Problem 1

Polygon \(Q\) is a scaled copy of Polygon \(P\).

2 4-sided polygons, P and Q. 1 side in polygon P is 4 and its corresponding side in Q is 3. Another side in polygon P is x, and its corresponding side in Q is y.
  1. The value of \(x\) is 6, what is the value of \(y\)?
  2. What is the scale factor?

Solution

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Problem 2

Figure \(f\) ​is a scaled copy of Figure \(e\) .

We know:

  • \(AB=6\)
  • \(CD=3\)
  • \(XY=4\)
  • \(ZW=a\)

Select all true equations.

2 figures, e and f. Figure e: segments A B and D C intersect at C. D C is 3, A B is 6. An ellipse through D. Figure f: segments X Y and Z W intersect at W. Z W is a. X Y is 4. An ellipse through Z.
A:

\(\frac{6}{3}=\frac{4}{a}\)

B:

\(\frac{6}{4}=\frac{3}{a}\)

C:

\(\frac{3}{4}=\frac{6}{a}\)

D:

\(\frac{6}{3}=\frac{a}{4}\)

E:

\(\frac{6}{4}=\frac{a}{3}\)

F:

\(\frac{3}{4}=\frac{a}{6}\)

Solution

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Problem 3

Solve each equation.

  1. \(\frac{2}{5}=\frac{x}{15}\)
  2. \(\frac{4}{3}=\frac{x}{7}\)
  3. \(\frac{7}{5}=\frac{28}{x}\)
  4. \(\frac{11}{4}=\frac{5}{x}\)

Solution

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Problem 4

Select the shape that has 180 degree rotational symmetry.

A:

Rhombus

B:

Trapezoid

C:

Isosceles trapezoid

D:

Quadrilateral

Solution

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(From Unit 2, Lesson 14.)

Problem 5

Name a quadrilateral in which the diagonal is also a line of symmetry. Explain how you know the diagonal is a line of symmetry. 

Solution

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(From Unit 2, Lesson 14.)

Problem 6

In isosceles triangle \(DAC\), \(AD\) is congruent to \(AC\) and \(AB\) is an angle bisector of angle \(DAC\). How does Kiran know that \(AB\) is a perpendicular bisector of segment \(CD\)?

Triangle A C D. Point B lies on side D C, and segment A B is drawn in. Sides D A and A C have single tick marks. Angles D A B and C A B have arcs with single tick marks.

Solution

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(From Unit 2, Lesson 8.)

Problem 7

In the figure shown, lines \(f\) and \(g\) are parallel. Select all angles that are congruent to angle 1.

Parallel lines f and g cut by a transversal, creating angles 1, 2, 3 and 4 at intersection of lines g and transversal, and creating angles 5, 6, 7 and 8 at intersection of lines f and transversal.
A:

1

B:

2

C:

3

D:

4

E:

5

F:

6

G:

7

H:

8

Solution

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(From Unit 1, Lesson 20.)