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Relationships Within Triangles - Printable Math Worksheets 9th - 10th Grade - Wayground

Relationships Within Triangles

Samantha Banwell

Created by Samantha Banwell

14 questions

9th - 10th Grade

Math

Updated Apr 2026

Relationships Within Triangles is a free printable mathematics worksheet for Grades 9–10 with 14 multiple-choice questions. Students identify and apply properties of triangle midsegments, medians, and altitudes, including finding unknown values, recognizing perpendicular relationships, and using slopes to determine a parallel or perpendicular side relationship. The worksheet also develops triangle reasoning through the triangle inequality, identifying the shortest side, and ordering sides and angles by their measures. Its varied diagram-based and numerical questions help students distinguish related triangle segments and connect geometric properties to calculations. An answer key is included for efficient review, independent practice, homework, or formative assessment.

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Relationships Within Triangles

Total questions: 14

Name
Class
Date
1.

The segment that connects the midpoints of two sides of a triangle is the _________.

a)

midsegment

b)

perpendicular bisector

c)

median

d)

altitude

2.
Segment WY is the mid segment of ΔQRS. Find the value of x.

Segment WY is the mid segment of ΔQRS. Find the value of x.

a)

34

b)

17

c)

68

d)

90

3.
Segment WY is the mid segment of ΔQRS. Find the value of x.

Segment WY is the mid segment of ΔQRS. Find the value of x.

a)

22

b)

11

c)

44

d)

90

4.
Segment WY is the mid segment of ΔQRS. Find the value of x.

Segment WY is the mid segment of ΔQRS. Find the value of x.

a)

12

b)

6

c)

24

d)

90

5.
The figure is an example of a(n) ...

The figure is an example of a(n) ...

a)

angle bisector

b)

dotted line theorem

c)

altitude

d)

median

6.
If A D ‾ \overline{AD} A D is the median of triangle ABC. What is the length of \ \overline{BC}\ if\ BD=15? B C i f B D = 1…

If  AD‾\overline{AD}  is the median of triangle ABC. What is the length of \ \overline{BC}\ if\ BD=15?  

a)

 152\frac{15}{2}  

b)

30

c)

15

d)

5

7.
The figures above are examples of ...

The figures above are examples of ...

a)

altitudes

b)

perpendicular bisectors

c)

medians

d)

angle bisectors

8.
B R ‾ \overline{BR}\ B R is the altitude of triangle ABC. If ∠ B R C = 9 x \angle BRC=9x ∠ B R C = 9 x find the value of x.

 BR‾ \overline{BR}\  is the altitude of triangle ABC. If  ∠BRC=9x\angle BRC=9x find the value of x. 

a)

90

b)

20

c)

9

d)

10

9.
B R ‾ \overline{BR} B R is the altitude of triangle ABC. If the slope of B R ‾ = 3 \overline{BR}=3 B R = 3 , what is the…

 BR‾\overline{BR} is the altitude of triangle ABC. If the slope of  BR‾=3\overline{BR}=3 , what is the slope of  AC‾\overline{AC} ? 

a)

3

b)

-3

c)

 −13-\frac{1}{3}  

d)

 13\frac{1}{3}  

10.

 AB=5, BC=13, CA=8AB=5,\ BC=13,\ CA=8  

Can you make a triangle with these side lengths?

a)

Yes

b)

No

11.

Sally is trying to draw a triangle. Her first two sides measure 7 in and 11 in. What length could she use for the third side of her triangle?

a)

20 in

b)

4 in

c)

8 in

d)

19 in

12.
Identify the shortest side measure.
Identify the shortest side measure.
a)
QP
b)
QM
c)
MP
13.
List the angles in order by measure, smallest to largest.
List the angles in order by measure, smallest to largest.
a)
∠B, ∠A, ∠C
b)
∠A∠,B, ∠C
c)
∠A, ∠C, ∠B
14.
List the sides in order from smallest to largest.

List the sides in order from smallest to largest.

a)

AB‾, BC‾, AC‾\overline{AB},\ \overline{BC},\ \overline{AC}

b)

AC‾, AB‾, BC‾\overline{AC},\ \overline{AB},\ \overline{BC}

c)

BC‾, AB‾, AC‾\overline{BC},\ \overline{AB},\ \overline{AC}

WaygroundAnswer Key

Relationships Within Triangles

Total questions: 14

1.
a)

midsegment

2.
c)

68

3.
b)

11

4.
a)

12

5.
d)

median

6.
b)

30

7.
a)

altitudes

8.
d)

10

9.
c)

 −13-\frac{1}{3}  

10.
b)

No

11.
c)

8 in

12.
b) QM
13.
c) ∠A, ∠C, ∠B
14.
b)

AC‾, AB‾, BC‾\overline{AC},\ \overline{AB},\ \overline{BC}

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FAQs

What does the Relationships Within Triangles worksheet cover?

This Grade 9–10 worksheet uses 14 multiple-choice questions to assess relationships among triangle midsegments, medians, and altitudes, along with triangle inequality and side-angle ordering. Students identify these segments, solve for missing lengths or angle values, use perpendicular slopes, determine whether side lengths form a triangle, and order sides or angles by measure.

How can I use this worksheet to teach relationships within triangles?

Introduce the segment vocabulary with diagrams, asking students to explain how a midsegment, median, and altitude differ before they begin the multiple-choice items. Then have students solve the midsegment and median length questions, justify the right-angle and slope answers for altitudes, and finish by discussing how the triangle inequality and side-angle relationships support the final questions.

What mistakes should I watch for when students complete this triangle relationships worksheet?

Students may confuse a midsegment, median, and altitude, or forget that a median divides the opposite side into two equal parts when finding a missing length. Watch for errors in recognizing an altitude as perpendicular, using the wrong sign or reciprocal for a perpendicular slope, accepting side lengths that fail the triangle inequality, and reversing the order of sides or angles.

How do I assign and grade this Relationships Within Triangles worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, so you can assign the 14 multiple-choice questions in the format that fits your lesson. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so diagram labels, measurement information, and multiple-choice options are easier to read. You can also apply a dyslexia-friendly font or translate the triangle relationships worksheet into another language.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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