Practice 1.9.3: Proving the Midsegment of a Triangle
Use your knowledge of midsegments to solve each problem.
1. Find the lengths of BC and XZ and the measure of ∠BZX.
continued
PRACTICE
UNIT 1 • SIMILARITY, CONGRUENCE, AND PROOFS
Lesson 9: Proving Theorems About Triangles
2. Find the lengths of BC and YZ and the measure of ∠AXY.
B
11.25
X
Z
A
10.5
72˚
Y
C
3. If AB = 10x – 5 and XY = 3x + 0.5, what is the length of XY?
continued
PRACTICE
UNIT 1 • SIMILARITY, CONGRUENCE, AND PROOFS
Lesson 9: Proving Theorems About Triangles
4. If AB = 6x + 6 and XY = 5x – 9, what is the length of AB?
(6x + 6)
Z
A
B
Y
(5x – 9)
X
C
5. The midpoints of a triangle are X (–2, –2), Y (–2, 3), and Z (5, 3). Find the
coordinates of the vertices of the triangle.
6. The vertices of a triangle are A (–2, 4), B (10, 2), and C (6, 8). Find the
coordinates of the midpoints of the triangle.
continued
PRACTICE
UNIT 1 • SIMILARITY, CONGRUENCE, AND PROOFS
Lesson 9: Proving Theorems About Triangles
1
BC .
7. Use a coordinate proof to show that EF BC and EF
2
=
y
10
9
8
7
6
5
4
3
B
2
1
-10 -9 -8
-6
-7
-5 4
-3 2
E
-1
0
-1
1
2
3
5
-2
-3
A
F
-4
-5
-6
-7
-8
-9
-10
C
4
6
8
7
9
10
x
continued
PRACTICE
UNIT 1 • SIMILARITY, CONGRUENCE, AND PROOFS
Lesson 9: Proving Theorems About Triangles
1
BC .
8. Use a coordinate proof to show that EF BC and EF
2
=
y
10
9
8
7
6
B
5
C
4
E
F
-10 -9
-8
-7 6
-5 4
-3 2
3
2
1
-1
0
-1
-2
A
-3
-4
-5
-6
-7
-8
-9
-10
1
5
2
3
4
6
8
7
9
10
x
continued
PRACTICE
UNIT 1 • SIMILARITY, CONGRUENCE, AND PROOFS
Lesson 9: Proving Theorems About Triangles
9. Determine the midpoints of AC and BC . Label the points E and F. Show that
1
EF AB and EF AB .
2
=
y
10
9
8
7
6
A
B
5
4
3
2
1
-10 -9
-8
-7 6
-5 4
-3 2
-1
0
-1
1
5
2
3
4
6
7
9
10
x
8
-2
-3
-4
-5
C
-6
-7
-8
-9
-10
continued
PRACTICE
UNIT 1 • SIMILARITY, CONGRUENCE, AND PROOFS
Lesson 9: Proving Theorems About Triangles
10. Determine the midpoints of AC and BC . Label the points E and F. Show that
1
EF AB and EF AB .
2
=
y
10
9
8
B
7
6
5
C
4
3
2
1
-10 -9
-8
-7 6
-5 - -3 -2
4
A
-1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
1
5
2
3
4
6
8
7
9
10
x
-10