H Secondary II
3.3 Worksheet
Name _________________________ Period _______
1. Write the theorem that justifies the truth of each statement.
a.
b.
2. Determine the value of x in each isosceles triangle.
a.
b.
3. Use the given information to answer each question.
a. When building a house, rafters are used to support the roof. The rafter shown in the diagram has the
shape of an isosceles triangle. In the diagram, 𝑁𝑃 ⊥ 𝑅𝑄, 𝑁𝑅 ≅ 𝑁𝑄, NP =12 feet, and RP=16 feet. Use
this information to determine the length of ̅̅̅̅
𝑁𝑄 . Explain.
b. While growing up, Nikki often camped out in her back yard in a pup tent.
A pup tent has two rectangular sides made of canvas, and a front and
back in the shape of two isosceles triangles also made of canvas. The
zipper in front, represented by ̅̅̅̅̅
𝑀𝐺    in the diagram, is the height of the
pup tent and the altitude of isosceles ∆𝐸𝑀𝐻. If the length of̅̅̅̅̅
𝐸𝐺   is 2.5
̅̅̅̅ ? Explain.
feet, what is the length of 𝐻𝐺
H Secondary II
4. Marcel is painting the triangular section of a
shuffleboard court shown in the figure. He starts
by putting 41 feet of tape around the outside of
the triangle. He knows that the base of the
triangle is 16 feet and each base angle of the
triangle measures 50 degrees. What is the length
of each leg?
5. Calculate the measure of ∠1. Show your work.
6. Calculate the measure of ∠1. Show your work.
7. For each pair of triangles, use the Hinge Theorem or its converse to write a conclusion using an inequality.
a.
b.
8. Given BD = 3, and DA = 4. Find h, a and b.
Hint: you will be using Pythagorean Theorem
C
twice.
a
h
B
D
b
A
9. Give the ordered pairs of the new polygon.
The vertices of triangle ABC are A (5, 3), B (2, 8),
and 𝐶 (−4, 5).
a)
b)
c)
d)
Reflect the triangle aver the x-axis
Reflect the triangle aver the y-axis
Rotate the triangle 180° about the origin
Translate the triangle left 5 and down 3.
H Secondary II
10. Determine if triangle ABC is similar to ADE.
Justify completely, using sentences.
11. Give the measure of angle OMN and QMN.
12. Give an appropriate name for the angle pairs:
a) 5 and 7
b) 2 and 3
c) 5 and 4
13. Write the equation of the line, then graph the line that passes through the points (-7, 4) and (-10, 4).
14. Given rectangle ACDE, calculate the measure of
.
H Secondary II
15. Prove the triangles are congruent.
G
a.
b.
D
F
H
Statements
Reasons
Statements
Reasons
Statements
Reasons
16. In the following figure triangle ABD is an isosceles
̅̅̅̅.
triangle, and ̅̅̅̅
𝐴𝐶 is perpendicular to 𝐵𝐷
Use a two-column proof to show that ∠𝐵 ≅ ∠𝐷.
H Secondary II
17. Fill in the measures of the remaining interior angles
on the diagram.
18. Solve for the measures of angle H and angle I.
29
82
135
19. Can we conclude triangle APQ is similar to
triangle ACB? Explain thoroughly.
20. Would the following side lengths form a right
triangle: 2.5 cm, 1.5 cm and 2 cm? Justify.
21. Given the following points: (-5, 0) and (4, -6).
Find the midpoint.
22. Given the following points: (-5, 0) and (4, -6).
Find the distance between them.