Two line segments AB and AC include an angle of 60 where AB = 5 cm and
AC = 7 cm. Locate points P and Q on AB and AC, respectively such thatAP=3 4AB And AQ=1 4AC respectively. Join P and Q and measure the length PQ.

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Solution

Using a protractor draw an angle BAC of measure $60 °$ such that AB = 5cm and AC =7cm

Since $A P = \frac{3}{4} A B$ , divide AB into 7 equal parts using the method of dividing a line segment into equal number of parts

Mark the third point from A as P

Since $A Q = \frac{1}{4} A C$ , divide AC into 5 equal parts using the method* of diving a line segment into equal number of parts .Mark the first point from A as Q.

Measure the distance from P to Q.

*To divide a line segment AB into a given number of parts, draw any ray from A and divide it into the reqired number of parts. Join the last arc (say point X) to the point B and then through each point on the ray draw lines parallel to BX.

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Q. Two line segments AB and AC include an angle of

60^{0}

where AB

= 5

cm and AC

= 7

cm. Locate points P and Q on AB and AC, respectively such that AP

= \frac{3}{4}

AB and AQ

= \frac{1}{4}

AC. Join P and Q and measure the length PQ.

Question 1
Two line segments AB and AC include an angle of $60^{\circ}$ , where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that $A P = \frac{3}{4} A B$ and $A Q = \frac{1}{4} A C$ .Join P and Q measure the length PQ.
Thinking Process
(i) Firstly we find the ratio of AB in which P divides, it with the help of the relation $A P = \frac{3}{4} A B$
(ii) Secondly, we find the ratio of AC in which Q divides. It with the help of the relation $A Q = \frac{1}{4} A C$ .
(iii) Now, construct the line segment AB and AC in which P and Q respectively divide it in the ratio from step (i) and (ii) respectively.
(iv) Finally get the point P and Q. After that join PQ and get the required measurement of PQ.

Question 1
Two line segments AB and AC include an angle of $60^{\circ}$ , where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that $A P = \frac{3}{4} A B$ and $A Q = \frac{1}{4} A C$ .Join P and Q measure the length PQ.
Thinking Process
(i) Firstly we find the ratio of AB in which P divides, it with the help of the relation $A P = \frac{3}{4} A B$
(ii) Secondly, we find the ratio of AC in which Q divides. It with the help of the relation $A Q = \frac{1}{4} A C$ .
(iii) Now, construct the line segment AB and AC in which P and Q respectively divide it in the ratio from step (i) and (ii) respectively.
(iv) Finally get the point P and Q. After that join PQ and get the required measurement of PQ.

Q. Draw an angle and label it as ∠BAC. Draw its bisector ray AX and take a point P on it. From P draw line segments PM and PN, such that PM ⊥ AB and PN ⊥ AC, where M and N are respectively points on rays AB and AC. Measure PM and PN. Are the two lengths equal?

∠BAC of △ABC is obtuse and AB=AC. P is a point on BC such that PC=12 cm. PQ and PR are perpendiculars to sides AB and AC respectively. If PQ=15 cm and PR=9 cm, then the length of PB (cm) is

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Two line segments AB and AC include an angle of 60 where AB = 5 cm andAC = 7 cm. Locate points P and Q on AB and AC, respectively such thatAP=3 4AB And AQ=1 4AC respectively. Join P and Q and measure the length PQ.

Two line segments AB and AC include an angle of 60 where AB = 5 cm and
AC = 7 cm. Locate points P and Q on AB and AC, respectively such thatAP=3 4AB And AQ=1 4AC respectively. Join P and Q and measure the length PQ.