Scholarship Geometry
Worksheet 4-1
Name:
In #1-6, classify each triangle by its angle measures.
1. ΔDBC (note: m<A = 59)
2. ΔABD
3. ΔADC
4. ΔBEA
use for #1-3
5. ΔDBC
6. ΔABC
use for #4-6
In #7-12, classify each triangle by its side lengths.
7. ΔEGH
8. ΔEFH
9. ΔHFG
use for #7-9
10. ΔPST
11. ΔRSP
12. ΔRPT
use for #10-12
In #13-16, find the side lengths of each triangle. Show all work.
13.
14.
(over)
15.
16.
Use the following information and the picture for #17-18.
A manufacturer makes trusses, or triangular supports,
for the roofs of houses. Each truss is the shape of an
isosceles triangle in which PQ PR . The length of the
4
base QR is the length of each of the congruent sides.
3
17. The perimeter of each truss is 60 ft.
Find each side length. Show all work.
18. How many trusses can a manufacturer make out of 150 feet of lumber?
19. A jeweler creates triangular earrings by bending
pieces of silver wire. Each earring is an isosceles triangle
with the dimensions shown. How many earrings can be
made from a piece of wire that is 50 cm long?
In #20-25, draw a sketch of each type of triangle or explain why it is not possible.
20. isosceles right
21. equiangular obtuse
22. scalene right
23. equilateral acute
24. scalene equiangular
25. isosceles acute
26. An equilateral triangle has a perimeter of 105 in. What is the length of each side?
In #27-28, classify each triangle by its angles and by its sides.
27. ΔABC
28. ΔACD
use for #27-28
29. An isosceles triangle has a perimeter of 34 cm. The congruent sides measure (4x – 1) cm. The
length of the third side is x cm. What is the value of x? Show all work.
30. Is every isosceles triangle equilateral? Is every equilateral triangle isosceles? Explain.
31. The average length of the sides of ΔPQR is 24.
How much longer than the average is the longest side?
32. Two sides of an equilateral triangle measure (y + 10) units and (y2 – 2) units. If the perimeter of
the triangle is 21 units, what is the value of y? (Show your work for this one on the back of this
paper.)