Midpoints and bisectors of segments and angles

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   On Ari's number line, A is at −7 and B is at 11. M is the midpoint of AB. What number is at M?

   • −2
   • 9
   • 4
   • 2
2. 2.

   On Bo's number line, A is at −3 and the midpoint M of AB is at 4. What number is at B?

   • −10
   • 1
   • 11
   • 7
3. 3.

   M is the midpoint of AB, for Esme's kite. AM = (3x + 2) m and MB = (5x − 8) m. What is AM?

   • 34 m
   • 17 m
   • 5 m
   • 8.5 m
4. 4.

   Ray BD bisects ∠ABC in Kira's drawing. m∠ABC = (8x + 4)° and m∠DBC = (5x − 4)°. What is m∠DBC?

   • 26°
   • 6°
   • 13°
   • 52°
5. 5.

   Ray BD bisects ∠ABC in Luz's drawing. m∠ABD = (3x + 11)° and m∠DBC = (7x − 29)°. What is m∠ABD?

   • 20.5°
   • 82°
   • 10°
   • 41°
6. 6.

   M is the midpoint of AB in Milo's diagram. Which statement must be true?

   • AM = AB
   • AM = MB
   • AB = ½ AM
   • ∠AMB = 90°
7. 7.

   Ray BD bisects ∠ABC in Noah's drawing. Which statement must be true?

   • m∠ABD = m∠ABC
   • BD ⊥ BA
   • m∠ABC = ½ m∠ABD
   • m∠ABD = m∠DBC
8. 8.

   Line ℓ is the perpendicular bisector of AB, and it meets AB at M. Which statement must be true for Pia's diagram?

   • AB = ½ AM, and ℓ is perpendicular to AB.
   • AM = AB, and ℓ is perpendicular to AB.
   • AM = MB, but ℓ may meet AB at any angle.
   • AM = MB, and ℓ meets AB at a right angle.
9. 9.

   M is the midpoint of AB and N is the midpoint of AM in Ren's drawing. AB = 24 cm. What is AN?

   • 3 cm
   • 6 cm
   • 12 cm
   • 18 cm
10. 10.

    P is the midpoint of AB and Q is the midpoint of PB. AB = 20 cm. What is AQ, for Tala's drawing?

    • 15 cm
    • 5 cm
    • 10 cm
    • 7.5 cm