Unit 7: Pre-Assessment & 7.1 Lesson Plan

Unit 7:

Pre-Assessment & Lesson 7.1

MT: Solving Applied Problems & Modeling in Geometry

Multiple Choice

LT: Use inverse operations to rationalize fractions.

Rationalize the following fraction: $$\frac{4}{\sqrt[]{5}}$$  

• $$\frac{\sqrt[]{4}}{5}$$  

• $$\frac{4\ \sqrt[]{5}}{5}$$  

• $$\frac{2\ \sqrt[]{5}}{5}$$  

• $$\frac{\sqrt[]{5}}{5}$$  

Multiple Choice

LT: Use inverse operations to rationalize fractions.

Rationalize the following fraction: $$\frac{\sqrt[]{2}}{\sqrt[]{3}}$$  

• $$\frac{\sqrt[]{6}}{3}$$  

• $$\frac{2\sqrt[]{3}}{3}$$  

• $$\frac{3\sqrt[]{2}}{3}$$  

• $$\frac{\sqrt[]{5}}{3}$$  

Multiple Choice

LT: Use Pythagorean Theorem to complete triangles.

Use the Pythagorean Theorem to find the missing side of this triangle, AC:

• 5.3 cm

• 4.7 cm

• 9.3 cm

• 8.1 cm

Multiple Choice

LT: Use Pythagorean Theorem to complete triangles.

Use the Pythagorean Theorem to find the missing side of this triangle, DE:

• 4.6 m

• 2.5 m

• 5 m

• 6.3 m

Multiple Choice

LT: Recognize and define specific vocabulary, such as sine, cosine, tangent.

Observe the given triangle. Which ratio represents the tangent of $$\angle C$$  ?

• $$\frac{3.4}{7}$$  

• $$\frac{7}{7.5}$$  

• $$\frac{7}{3.4}$$  

• $$\frac{7.5}{3.4}$$  

• $$\frac{3.4}{7.5}$$  

Multiple Choice

LT: Recognize and define specific vocabulary, such as sine, cosine, tangent.

Observe the given triangle. Which ratio represents the sine of $$\angle C$$  ?

• $$\frac{3.4}{7}$$  

• $$\frac{7}{7.5}$$  

• $$\frac{7}{3.4}$$  

• $$\frac{7.5}{3.4}$$  

• $$\frac{3.4}{7.5}$$  

Multiple Choice

LT: Recognize and define specific vocabulary, such as sine, cosine, tangent.

Observe the given triangle. Which ratio represents the cosine of $$\angle C$$  ?

• $$\frac{3.4}{7}$$  

• $$\frac{7}{7.5}$$  

• $$\frac{7}{3.4}$$  

• $$\frac{7.5}{3.4}$$  

• $$\frac{3.4}{7.5}$$  

Unit 7 Lesson 7.1:

Rationalizing Fractions & Pythagorean Theorem

Take notes as you go!

Rationalizing Fractions NOTES

​Rationalize means to eliminate irrational numbers when they show up in the denominator part of a fraction.

When fractions have square roots in the denominator, that is a HUGE problem. They will look something like this:  

Rationalizing Fractions NOTES

​STEPS to RATIONALIZING:

Step 1: Identify the denominator​.

Step 2: Multiply the fraction by ​

Step 3: Multiply straight across the fractions.

Step 4: Simply the numerator & denominator. ​

Rationalizing Fractions EXAMPLE

​Step 2: Multiply the fraction by

Rationalizing Fractions EXAMPLE

Step 4: Simplify the numerator & denominator (this part is EXTREMELY important so read each part CAREFULLY)

​

​

Rationalizing Fractions EXAMPLE

Multiple Choice

Rationalize $$\frac{12}{\sqrt[]{3}}$$  .

• $$\frac{4\ \sqrt[]{3}}{3}$$  

• $$3\ \sqrt[]{3}$$  

• $$\frac{3\ \sqrt[]{3}}{3}$$  

• $$4\ \sqrt[]{3}$$  

Multiple Choice

Rationalize $$\frac{7}{\sqrt[]{5}}$$  .

• $$\frac{7\ \sqrt[]{5}}{5}$$  

• $$7\ \sqrt[]{5}$$  

• $$\frac{\sqrt[]{5}}{5}$$  

• $$\frac{5\ \sqrt[]{7}}{7}$$  

Multiple Choice

Rationalize $$\frac{2\ \sqrt[]{5}}{\sqrt[]{2}}$$  .

• $$\frac{2\ \sqrt[]{10}}{5}$$  

• $$\sqrt[]{10}$$  

• $$\frac{4\ \sqrt[]{5}}{2}$$  

• $$\sqrt[]{5}$$  

Multiple Choice

Rationalize $$\frac{3\ \sqrt[]{3}}{\sqrt[]{3}}$$  .

• $$3\ \sqrt[]{3}$$  

• $$9$$  

• $$3$$  

• $$6\ \sqrt[]{3}$$  

Pythagorean Theorem NOTES

​The Pythagorean Theorem can be used to calculate the missing sides of RIGHT TRIANGLES.

​Pythagorean Theorem Formula & Model: ​

​FORMULA

​MODEL

Pythagorean Theorem NOTES

Breakdown: Each right triangle has 2 legs and the longest side is the hypotenuse.

Pythagorean Theorem NOTES

Pythagorean Theorem NOTES

Pythagorean Theorem EXAMPLE

Pythagorean Theorem EXAMPLE

Multiple Choice

Find the length of JL.

• 16.6

• 25

• 12.5

• 19.3

Multiple Choice

Find the length of AC.

• 22

• 38

• 26

• 13

Multiple Choice

Find the length of ST.

• 5.4

• 7.6

• 8.5

• 6.8