iCoachMath.com: Examples on Segment and Angle Bisectors - Introduction to Geometry

Curriculum: Alaska Math Grade Level Expectations Click to change Curriculum

Topic: Introduction to Geometry Click to change Topic

Lesson: [9] G-1, [10] G-8: Segment and Angle Bisectors Click to change Lesson

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e The midpoint of AB is (- 7, - 1)and one of the end point is A(- 1, 1). Find the coordinates of the other end point. e

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e Find the measures of ∠DAB and ∠BCD. [Given x = 29.]
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e In ΔDCE, EP¯ is the angle bisector of ∠DEC as shown. Find m∠PEC. [ax - b = 5x - 6 and cx + d = 3x + 4] e

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e Find the coordinates of the midpoint of XY¯. The endpoints of XY¯ are X(- 1, 9) and Y(8, -6). e

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e Is DE¯ the segment bisector of AC¯? [Given a = 15 cm and b = 16 cm.]
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e SQ→ is the bisector of ∠PSR. Find the m∠QSR and m∠PSR. m∠PSQ = x. [Given x = 79.] e

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e In the figure, C is the mid point of AB¯ and D is the midpoint of CB¯. If AB¯ = 36 inches and CD¯ = 2x + 1, then find the value of x.
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e In the given figure, OC¯ is the angle bisector of ∠AOB and OD¯ is the angle bisector of ∠COB. If ∠AOC= (3y - 2)^o and ∠COD = 26^o, then find the value of y.
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e In the figure shown, AD→ is the angle bisector of ∠BAC, AE→ is the angle bisector of ∠DAC and AF→ is the angle bisector of ∠BAD. If m∠BAC = 64, then find m∠FAE.
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e OP→ is the bisector of ∠AOB. Find the measure of ∠POB. [Given x = 118] e

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e OB→ is the angular bisector of ∠AOC. Find the value of k.
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e AB→ bisects ∠CAD; m∠CAB = 35; what is the measure of ∠BAD? e

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e AB is a line segment whose length is 10cm. P is the mid-point of AB¯. Find the length of AP¯. e

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e In the figure, C is the mid point of AB¯ and D is the midpoint of CB¯. If AB¯ = 40 inches and CD¯ = 2x + 4, then find the value of x.
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e Select the correct statement / statements.
1. An angle bisector is a line.
2. An angle bisector is a line of symmetry for the two arms.
3. An angle bisector is equidistant from both the arms of the angle it bisects.
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e The midpoint of AB is (- 5, - 1)and one of the end point is A(- 1, 1). Find the coordinates of the other end point. e

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e Identify the correct statement. e

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e Point C is the midpoint of AB¯. Which of the following is not true?
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e Which of the following is true? e

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e Is DE¯ the segment bisector of AC¯? [Given a = 18 cm and b = 19 cm.]
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e Which of the following is the perpendicular bisector of AB¯? e

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e S is the midpoint of NR¯. Which of the following is true? e

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e Find the coordinates of the midpoint of XY¯. The endpoints of XY¯ are X(- 4, 7) and Y(6, -4). e

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e Identify the angle bisector of ∠ACB.
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e CD↔ is the perpendicular bisector of AB¯ at point P. Name two congruent angles.
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e SQ→ is the bisector of ∠PSR. Find the m∠QSR and m∠PSR. m∠PSQ = x. [Given x = 78.] e

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e Which of the following figures show that OC→ is the angle bisector of ∠AOB?
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e Points A, B, C, D, E are collinear, C is the mid point of AB¯. D is the mid point of AC¯ and E is the midpoint of AD¯. Then find the ratio AEAB.
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e In the figure, C is the mid point of AB¯ and D is the midpoint of CB¯. If AB¯ = 32 inches and CD¯ = 2x + 4, then find the value of x.
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e In the given figure, OC¯ is the angle bisector of ∠AOB and OD¯ is the angle bisector of ∠COB. If ∠AOC= (3y - 3)^o and ∠COD = 24^o, then find the value of y.
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BB In ΔDCE, EP¯ is the angle bisector of ∠DEC as shown. Find m∠PEC. [ax - b = 6x - 7 and cx + d = 4x + 5] BB

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BB When we bisect an obtuse angle, what type of angles do we get? BB

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BB Find the measures of ∠DAB and ∠BCD. [Given x = 28.]
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BB Use the marks on the figure to identify the correct statements.
I. AD¯ ≅ CD¯
II. ∠ADB ≅ ∠BDC
III. AC¯ ≅ AD¯
IV. BD¯ ⊥AC¯
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BB In the figure shown, AD→ is the angle bisector of ∠BAC, AE→ is the angle bisector of ∠DAC and AF→ is the angle bisector of ∠BAD. If m∠BAC = 62, then find m∠FAE.
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