Angle Bisector

Q.

How to construct an angle of 50 degrees

Q. Choose the correct ratio for the angle bisector theorem for this triangle.

1. $\frac{AB}{AC}=\frac{AD}{AC}$
2. $\frac{BD}{DC}=\frac{AB}{AC}$
3. $\frac{DC}{AC}=\frac{AD}{BD}$
4. $\frac{AB}{AD}=\frac{BC}{BD}$

Q. Construct △DEF such that DE = 12 cm, DF = 5 cm and ∠EDF = 90⁰. Also, measure the length of the side EF.

Q.

Hari was asked to bisect a given angle, $\angle$ BOA as shown. He has done the following steps:
He draws an arc with centre O and some radius such that it cuts OB and OA at D and C respectively. Then he draws two more arcs with centres as C and D and radius more than $\frac{1}{2}$CD as shown (intersecting at Y) but has no idea why.

Select the correct statement which explains to him the reason for his construction.

Statement A : Because of equal radius, DY = CY and OD = OC. So $△$ DOY is congruent to $△$ COY

Statement B : Since OC = OD, $△$ ODC in an isosceles triangle, base angles are equal.

1. Statements A and B are true, only Statement A explains the reason.
2. Statements A and B are true, only Statement B explains the reason.
3. Statements A and B are true, but none explains the reason.
4. Statements A and B are false.

Q. Number of arcs to be drawn to construct an angle bisector =

1. 2
2. 3
3. 4

Q. A/An_______equidistant from the sides of the angle when measured along a segment perpendicular to the sides of the angle.

1. Altitude
2. Perpendicular
3. Perpendicular bisector
4. Angle bisector

Q. Fill in the blanks:
(i) Two line segments are congruent if .......
(ii) Two angles are congruent if ......
(iii) Two squres are congruent if .......
(iv) Two rectangles are congruent if .......
(v) Two circles are congruent if .......

Q. Construct △DEF such that DE = 12 cm, DF = 5 cm and ∠EDF = 90⁰. Also, measure the length of the side EF.

Q. The angle formed when a straight angle is bisected is called _________.

1. an acute angle
2. an obtuse angle
3. a reflex angle
4. a right angle

Q. In the adjacent figure ray OS stands on a line PQ. Ray OR and ray OT are angle bisectors of $\angle POS$ and $\angle SOQ$ respectively. Find $\angle ROT$.

Q. The straight lines $AB$ and $CD$ intersect at $E$. If $EF$ and $EG$ are bisectors of $\angle DEA$ and $\angle AEC$
respectively and if $\angle AEF=x$ and $\angle AEG=y$, then

1. $x+y<{90}^o$
2. $x+y>{90}^o$
3. $x+y={90}^o$
4. $x+y={180}^o$