Lesson 1 Leaping Lizards! Develop Understanding

Ready

For each of the right triangles, determine the measure of the missing side. Leave the measures in exact form if irrational.

1.

A right triangle with hypotenuse labeled with a question mark, shorter leg labeled 3, and longer leg labeled 4. ?

2.

A right triangle with hypotenuse labeled with a question mark, shorter leg labeled 5, and longer leg labeled 12.

3.

A right triangle with hypotenuse labeled 4, shorter leg labeled 1, and longer leg labeled with a question mark.

4.

A right triangle with hypotenuse labeled radical 10, shorter leg labeled with a question mark, and longer leg labeled 3.

5.

A right triangle with hypotenuse labeled radical 17, shorter leg labeled with a question mark, and longer leg labeled 4.

6.

A right triangle with hypotenuse labeled radical 13, shorter leg labeled 2, and longer leg labeled with a question mark.

Set

Use the images and pre-images of the insects on the grids shown to answer the problems. You may sketch on the grids to show attributes of the transformation to assist yourself in the work.

7.

Name the single transformation that can be used to carry the pre-image to the image for each pair of insects.

a.

A coordinate plane with x- and y- axis labeled in 1-unit increments. A vertical ant labeled pre-image in Quadrant I and a left-facing ant labeled image in Quadrant II. x–2–2–2222444y–2–2–2222444000pre-imageimage

b.

A coordinate plane with x- and y- axis labeled in 1-unit increments. A left-facing grasshopper labeled pre-image in Quadrant III and a right-facing grasshopper labeled image in Quadrant IV. x–4–4–4–2–2–2222444y–4–4–4–2–2–2222000pre-imageimage

c.

A coordinate plane with x- and y- axis labeled in 1-unit increments. A right-facing ladybug labeled pre-image mostly located in Quadrant II and a right-facing ladybug labeled image in Quadrant IV. x–6–6–6–4–4–4–2–2–2222444666y–4–4–4–2–2–2222444000pre-imageimage

8.

Consider the connection between corresponding points for each of the transformations, to visualize the pathway the points might follow between image and pre-image, which of the following statements are true and which are false. Draw a sketch to accompany your response.

a.

In a reflection, pairs of corresponding points lie on parallel lines.

True or False?

b.

In a translation, pairs of corresponding points are on parallel lines.

True or False?

c.

In a rotation, pairs of corresponding points are on parallel lines.

True or False?

d.

In a reflection, pairs of corresponding points lie on segments perpendicular to the line of reflection.

True or False?

e.

In a rotation, pairs of corresponding points lie on concentric circles.

True or False?

f.

In a translation, pairs of corresponding points lie on concentric circles.

True or False?

Perform each of the transformations as described. Focus on anchor points!

9.

Translate the grasshopper right and up .

A coordinate plane with x- and y- axis labeled in 1-unit increments. A left facing grasshopper labeled pre-image in Quadrant III . x–4–4–4–2–2–2222444y–4–4–4–2–2–2222000pre-imageimage

10.

Reflect the ant over the line . Create anchor points as needed.

A coordinate plane with x- and y- axis labeled in 1-unit increments. A vertical ant labeled pre-image in Quadrant I and the line y=-x 2. x–4–4–4–2–2–2222444y–4–4–4–2–2–2222444000pre-imageimage

Go

Graph each function on the coordinate grid provided.

11.

A coordinate plane with x- and y-axis in 1-unit increments. x–5–5–5555y–5–5–5555000

12.

A coordinate plane with x- and y-axis in 1-unit increments. x–5–5–5555y–5–5–5555000

13.

State at least one similarity and one difference between the functions and .

14.

A coordinate plane with x- and y-axis in 1-unit increments. x–5–5–5555y–5–5–5555000

15.

A coordinate plane with x- and y-axis in 1-unit increments. x–5–5–5555y–5–5–5555000

16.

State at least one similarity and one difference between the functions and .

17.

A coordinate plane with x- and y-axis in 1-unit increments. x–5–5–5555y–5–5–5555000

18.

A coordinate plane with x- and y-axis in 1-unit increments. x–5–5–5555y–5–5–5555000

19.

State at least one similarity and one difference between the functions and .