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WorksheetsChapter 5: Relationships in Triangles
Total questions: 24
Worksheet time: 12mins
On a school playground a triangular-shaped sand box is built as shown here. Can a sand castle be built at the circumcenter and still be inside the sand box?
No, the circumcenter of an acute triangle is on the edge of the triangle.
Yes, the circumcenter of an acute triangle is inside the triangle.
More information is needed, such as the length of the sides of the triangle.
No, the circumcenter of an acute triangle is outside the triangle.
Find the measure of AD.
12
11.5
23
6
Find the measure of angle FGH.
99°
33°
66°
50.5°
Find the measure of ML.
22
11
10
5
In triangle GIK, ML = 7. Find IM.
7
14
28
21
A local artist is designing a triangular piece of metal art that will balance on a pole. In his design, on the coordinate plane, the vertices are located at (−2, 2), (1, −3), and (1, 7). What are the coordinates of the point where the artist should place the pole under the triangle so that it will balance?
(1, 3)
(−1, 2)
(0, 2)
(1, 1)
The vertices of triangle LMN are L(-4, 3), M(2, 3), and N(-1, -2). Find the coordinates of the orthocenter.
(-1, 6/5)
(-1, 8/3)
(-1, -1)
(-1, 7/4)
In triangel TVX, Z is the centroid and TW = 72. Find TZ and ZW.
TZ = 36 and ZW = 36
TZ = 24 and ZW = 48
TZ = 48 and ZW = 24
TZ = 56 and ZW = 16
In the figure shown, angle 1 is an exterior angle of triangle XYZ. Which statement is correct?
angle 1 + angle 3 < 180
angle 4 > angle 1
angle 1 > angle 2
angle 3 > angle 1
Choose the possible measure for angle 1 in the figure shown.
180°
0°
11°
110°
Refer to the figure shown. What is the longest segment in triangle ABC?
segment BD
segment AB
segment AC
segment BC
Refer to the figure. Is LK longer than LJ? Explain.
Yes; the measure of the angle opposite LK is 90 and the measure of the angle opposite LJ must be less than 90 because the sum of the measures of the angles must be 180.
Yes; LK is the hypotenuse of triangle LJK, and LJ is a leg.
Yes; the shortest distance from a point to a line is a perpendicular segment.
All of these.
State the assumption that could be used to start an indirect proof of the statement if x is an odd integer, then 3x is an odd integer.
3x is an odd integer.
3x is an even integer.
x is an even integer.
x is an odd integer.
Which assumption would you make to start an indirect proof of the following statement? The majority of students surveyed preferred chocolate ice cream to vanilla ice cream.
The number of students surveyed that preferred chocolate ice cream to vanilla ice cream was greater than 25%.
The number of students surveyed that preferred chocolate ice cream to vanilla ice cream was greater than 50%.
The number of students surveyed that preferred vanilla ice cream to chocolate ice cream was greater than 25%.
The number of students surveyed that preferred vanilla ice cream to chocolate ice cream was greater than 50%.
What is another name for an indirect proof?
proof by contradiction
paragraph proof
default proof
proof by assumption
State the assumption that could be used to start an indirect proof of the statement AB + BC > DE.
AB + BC < DE
AB + BC > DE
AB + BC < DE
AB + BC = DE
The _______________ states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Definition of an Inequality
Definition of a Triangle
Triangle Inequality Theorem
Triangle Equality Theorem Triangle Equality Theorem
Is it possible to draw a triangle with sides measuring 13, 21, and 39? Explain
No; 39 is greater than 13 + 21.
No; 13 is less than 21 + 39.
Yes; the sides of the triangle are not all the same lengths.
Yes; 13 + 21 is less than 39.
If the measures of two sides of a triangle are 3 and 1, between what two numbers must the measure of the third side fall?
1 and 3
1 and 7
2 and 4
2 and 5
Marty has a piece of rope with exactly 7 knots tied at equal intervals as shown. Using the ENTIRE rope, he wants to make triangles so that each vertex of the triangle occurs at a knot. How many different triangles can Marty make?
4
1
2
3
In the figure, angle B > angle Y. Which of the following gives the relationships between AC and XZ?
AC < XZ
AC < XZ
AC = XZ
AC > XZ
If MR is congruent to NR, which relationship is true?
angle PRN = 2 (angle MRP)
angle PRN > angle PRM
angle PRN is congruent to angle MRP
angle PRN < angle MRP
Write an inequality to describe the possible values of x.
x > 20
x < 17
x < 20
x > 17
Which inequality describes the range of possible values for x?
x < 14
4 < x < 14
x < 4 and x > 14
- 6 < x < 14
