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

Curriculum: Alabama Course of Study Click to change Curriculum

Topic: Introduction to Geometry Click to change Topic

Lesson: 2: 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 A line that is perpendicular to a segment at its midpoint is known as
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e What is the angle between the interior angle bisector and the exterior angle bisector of the angle formed by two rays? e

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e How many equidistant points are lying on the angular bisectors of two intersecting lines AB and CD at a distance of 5 cm from their point of intersection? 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 In figure, if XOY¯ is a line, OQ¯ bisects ∠COY and ∠POQ is right angle then prove that OP¯ bisects the ∠XOC.
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e What is the locus of a point equidistant from two intersecting lines? e

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e If an obtuse angle is bisected, then the resulting two angles are _________.
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e How many number of points are there which are lying on the perpendicular bisector of a line segment and are at a distance of 5 cm from the line segment? e

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e If OC¯, OD¯ and OE¯ are the angular bisectors of ∠AOB, ∠AOC and ∠DOC respectively, then find α.
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e ON¯ and OM¯ are the interior and exterior angle bisectors of ∠AOB respectively. If ∠AON = 30^o, then ∠MOA is e

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e ON¯ and OM¯ are the interior and exterior angle bisectors of ∠AOB respectively. If ∠MOB = 110^o, then ∠NOB equals
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e P and M are the points on the perpendicular bisector of AB¯. If ∠PAB > ∠MAB, then which of the following is true?
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e Find the angle made by the angular bisector of the angle between OF₂ and OF₄ with the vertical.
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e Find m∠BFC if BF and CF are the angle bisectors of ∠CBD and ∠BCE.
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e If OC¯, OD¯, OE¯, OF¯, OD¯′, OE¯′ and OF¯′ are the angular bisectors of ÐAOB, ÐCOB, ÐDOB, ÐEOB, ÐAOC, ÐAOD′ and ÐAOE′ respectively, then find the value of (α+βα-β). e

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e OB is the angle bisector of ∠COA. If ∠BOA = 40^o. Find ∠COD. e

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e Is BM→ an angle bisector of AC?
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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 Find the number of angular bisectors that can be drawn to the given figure. e

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e Which of the following is true? e

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e OQ and OR are the bisectors of ∠RQS and ∠QRT, what is the measure of ∠P?
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e In figure, if XOY¯ is a line, OQ¯ bisects ∠COY and ∠POQ is right angle then prove that OP¯ bisects the ∠XOC.
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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 AD¯ is the bisector of ∠BAC. AE¯ is the bisector of ∠BAD. What is the ratio of m∠BEA to m∠BDA? e

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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 The lines OP¯, OQ¯ makes an angle 75° and 32°respectively with the horizontal in the same direction. Find the angle made by the angular bisector of ∠POQ with the horizontal.
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e Find the ratio of angles (measured from horizontal) made by the angular bisectors of the angles made by OX¯, OY¯ and OP¯, OQ¯.
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e Choose the relation between x and y such that BD¯ is the angular bisector in the given figure.
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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 CE bisects ∠ACD. CF bisects ∠ACE. Find the measure of ∠BAC if BC¯ || AE¯ e

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e Identify the angle bisector of ∠ACB.
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e QT→ and QS→ are the bisectors of ÐPQS and ÐRQT. Find mÐSQT.
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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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e In ΔDCE, EP¯ is the angle bisector of ∠DEC as shown. Find m∠PEC. [ax - b = 6x - 7 and cx + d = 4x + 5] e

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

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e Find the measures of ∠DAB and ∠BCD. [Given x = 28.]
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e 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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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 = 62, then find m∠FAE.
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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 OC→ is the bisector of right angle AOB. m∠AOC is ... e

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e Which figure shows a bisector?
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e What is the best name for MN¯ in the figure shown? e