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Isosceles and Equilateral Triangles and Triangle Inequalities (Due 2-17-22)

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Essential Question: How can we determine the angles and side lengths of Isosceles and Equilateral Triangles. Learning Target: Students will be able to calculate the angles and side lengths of Isosceles and Equilateral Triangles. Complete the entire document and show all work for full credit.

Part I

Isosceles and Equilateral Triangles

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Otázka 1
1.

Find the measure of the indicated angle.

m∠C=

m∠A=

Otázka 2
2.

Solve for x.

Find the measure of the indicated angle.

x=

m∠T=

m∠R=

Otázka 3
3.

Solve for x.

Find the measure of the indicated angle.

x=

m∠C=

m∠B=

Otázka 4
4.

Solve for x.

Find the length of the indicated side.

x=

DE=

m∠E=

Otázka 5
5.

Solve for x.

Find the length of the indicated side.

x=

OM=

m∠G=

Otázka 6
6.

Solve for x.

Find the length of the indicated side.

x=

KL=

m∠J=

Otázka 7
7.

A regular pentagon has five congruent sides and five 108° angles, as

shown in the figure. Find the angle measures: x = ; y = ;

z =

Part II

Triangle Inequalities

Otázka 8
8.

Determine if the side lengths could form a triangle. Use an inequality to prove your answer.

16 m, 21 m, 39 m

Otázka 9
9.

Determine if the side lengths could form a triangle. Use an inequality to prove your answer.

18 in, 6 in, 13 in

+ =; and 19 18

Therefore this a triangle

Otázka 10
10.

Is it possible to have a triangle with sides of 6cm, 4cm, and 3cm?

Otázka 11
11.

Find the range of possible values for x using the Triangle Sum Theorem from your page 5 notes.

<x<

Otázka 12
12.

Find the range of possible values for x using the Triangle Sum Theorem from your page 5 notes.

<x<

Otázka 13
13.

In △ PQR, PQ = 3x + 1, QR = 2x − 2, and PR = x + 7. Determine the range of possible values of x.

Use the Triangle Sum Theorem from your page 5 notes.

≤ x <

Otázka 14
14.

For each triangle, write the order of the angle measures from least to greatest.

Be sure to include the angle symbol in your answer. ----> ∠ <----

< <

Otázka 15
15.

For each triangle, write the order of the angle measures from least to greatest.

Be sure to include the angle symbol in your answer. ----> ∠ <----

< <

Otázka 16
16.

Suppose a triangle has side lengths PQ, QR, and PR, where PR = 2PQ = 3QR. Write the angle measures in order from least to greatest.

Be sure to include the angle symbol in your answer. ----> ∠ <----

< <

Otázka 17
17.

For each triangle, write the side lengths in order from least to greatest.

< <

Otázka 18
18.

For each triangle, write the side lengths in order from least to greatest.

< <