Lesson 5 Parallelism Preserved and Protected Solidify Understanding

Ready

1.

Use what you know about triangles to write a paragraph proof that proves the sum of the angles in a quadrilateral is . Support your justification with a diagram.

2.

Find the measure of in quadrilateral .

Quadrilateral with one angle labelled 7x-3, one angle 6x-5, one angle 16x 15, and one angle 4x 23.

For problems 3–7, use the graph of lines , , , and .

A coordinate plane with x- and y-axis of 1-unit increments. Line p has y intercept of 2 and slope of -3/4, line q has y intercept of 4 and slope of -3/4, line r has y intercept of 4 and slope of 3/4, and line s has y intercept of 2 and slope of 3/4. x–5–5–5555y–5–5–5555000

3.

Find the equation of each line.

4.

Which, if any, of the lines are parallel? How do you know?

5.

Which, if any, of the lines are perpendicular? How do you know?

6.

Find the coordinates of the intersection of lines and .

7.

  • Classify the shape made by the intersection of the 4 lines.

  • List as many observations as you can about the shape and its features.

  • Use the attributes of the shape to find the intersection of lines and .

Set

8.

Verify the parallel postulates below by naming the line segments in the pre-image and its image that are still parallel. Use correct mathematical notation.

a.

After a translation, corresponding line segments in an image and its pre-image are always parallel or lie along the same line.

A star with points E,F,G,H, J and star E'F'G'H'J' translated to the right.

b.

After a rotation of , corresponding line segments in a pre-image and its image are parallel or lie on the same line.

A star with points E,F,G,H, J and star E'F'G'H'J' rotated 180 degrees around point M.

c.

After a reflection, line segments in the pre-image that are parallel to the line of reflection will be parallel to the corresponding line segments in the image.

A star with points E,F,G,H, J and star E'F'G'H'J' reflected over a line.

Go

Find the complement and the supplement of the given angles. It is possible that the angle does not have a complement or supplement.

9.

10.

11.

12.

13.

14.

Perform each transformation, given the pre-image and description or rule.

15.

Translate ,

A coordinate plate with x- and y- axis of 1-unit increments with Triangle ABC with A(5,5), B(7,3), and C(4,0). x–5–5–5555y–5–5–5555000AAABBBCCC

16.

Rotate counterclockwise around the point

A coordinate plate with x- and y- axis of 1-unit increments with Triangle ABC with A(-5,-4), B(-2,-4), and C(-4,-2). x–5–5–5555y–5–5–5555000AAABBBCCCPPP

17.

Reflect over the line

A coordinate plate with x- and y- axis of 1-unit increments with Triangle XYZ with X(1,1), Y(5,3), and Z(2,4) and line y=x 3 x–5–5–5555y555101010000XXXYYYZZZ

18.

Translate ,

A coordinate plate with x- and y- axis of 1-unit increments with Triangle PQR with P(-3,6), R(-4,1), and Q(-6,5). x–5–5–5555y–5–5–5555000PPPQQQRRR