Lesson 1: Angles and Steepness

Learning Target: I can explain why knowing one acute angle in a right triangle determines the ratio of the side lengths.

Fill in the Blanks

Triangle ABC is similar to triangle DEF. Write as many equations as you can to describe the relationships between the sides and angles of the 2 triangles.

$\angle\ A\ \cong\angle\$

Fill in the Blanks

Triangle ABC is similar to triangle DEF. Write as many equations as you can to describe the relationships between the sides and angles of the 2 triangles.

$\angle\ B\ \cong\angle\$

Fill in the Blanks

Triangle ABC is similar to triangle DEF. Write as many equations as you can to describe the relationships between the sides and angles of the 2 triangles.

$\angle\ C\cong\angle\$

Fill in the Blanks

Triangle ABC is similar to triangle DEF. Write as many equations as you can to describe the relationships between the sides and angles of the 2 triangles.

$\frac{AB}{DE}=\frac{BC}{?}$

Fill in the Blanks

Triangle ABC is similar to triangle DEF. Write as many equations as you can to describe the relationships between the sides and angles of the 2 triangles.

$\frac{AB}{DE}=\frac{?}{FD}$

Fill in the Blanks

Triangle ABC is similar to triangle DEF. Write as many equations as you can to describe the relationships between the sides and angles of the 2 triangles.

$\frac{CB}{CA}=\frac{FE}{?}$

Math Response

$$\Delta ABC$$ is a right triangle. Therefore, you can use the Pythagorean Theorem.

$$a^2+b^2=c^2$$

Find the value of $$x.$$

Use "x = "

Type answer here

Correct Answer: x=\sqrt{34}

Deg^°

Rad

Math Response

Find the value of $$y.$$

Use "y = "

Type answer here

Correct Answer: y=\sqrt{20}

Deg^°

Rad

Open Ended

Find the value of z.

If there is not enough information, what else do you need to know?

Dropdown

If we had a triangle with the same angles as Δ GHJ but different side lengths, would that be helpful for finding z? ​

Select answer

, then we could use the ​

Select answer

to find z.

Multiple Choice

Which equation would you use to find x?

• $$\frac{1}{28}=\frac{x}{12}$$

• $$\frac{1}{28}=\frac{x}{4.8}$$

• $$\frac{12}{28}=\frac{1}{x}$$

• $$\frac{x}{12}=\frac{28}{1}$$

Fill in the Blanks

What is the value of x ?

inches.

Fill in the Blanks

How can you use the ratio to generate the horizontal length of the ramp given the vertical length, y =

inches (round to the nearest whole number.

Drag and Drop

Does every angle in a right triangle give you a fixed ratio of vertical length to horizontal length?

​

Placeholder

, because when you’re dealing with right triangles, all the triangles with the same angle measure for one of the other angles are ​

Placeholder

, so they have the ​

Placeholder

ratios.

Drag these tiles and drop them in the correct blank above

Yes

No

similar

same

different