Math  /  Geometry

Question9. Construct two line segments of lengths AB=4.4 cmA B=4.4 \mathrm{~cm} and CD=2.8 cmC D=2.8 \mathrm{~cm}. Then construct the following line segments. (a) XY=2CDX Y=2 C D (b) PQ=AB+CDP Q=A B+C D
10. If PQ=2 cmP Q=2 \mathrm{~cm} and RS=2.5 cmR S=2.5 \mathrm{~cm}, then construct a line segment whose length is equal to (a) PQ+RSP Q+R S (b) 2 PQ (c) RS - PQ

Studdy Solution

STEP 1

1. We have a ruler and a compass for constructing line segments.
2. The lengths given are accurate and can be measured precisely.
3. We understand basic geometric constructions.

STEP 2

1. Construct line segments AB=4.4cm AB = 4.4 \, \text{cm} and CD=2.8cm CD = 2.8 \, \text{cm} .
2. Construct line segment XY=2×CD XY = 2 \times CD .
3. Construct line segment PQ=AB+CD PQ = AB + CD .
4. Construct line segment PQ+RS PQ + RS .
5. Construct line segment 2×PQ 2 \times PQ .
6. Construct line segment RSPQ RS - PQ .

STEP 3

Use a ruler to draw a line segment AB AB of length 4.4cm 4.4 \, \text{cm} .

STEP 4

Use a ruler to draw a line segment CD CD of length 2.8cm 2.8 \, \text{cm} .

STEP 5

To construct XY=2×CD XY = 2 \times CD , measure CD CD using a compass. Without changing the compass width, place the compass point on X X and mark an arc. Then, place the compass point on the arc and mark another arc. Draw a line segment XY XY through these points.

STEP 6

To construct PQ=AB+CD PQ = AB + CD , measure AB AB using a compass. Place the compass point on P P and draw an arc. Then, measure CD CD using the compass, place the compass point on the arc, and draw another arc. Draw a line segment PQ PQ through these points.

STEP 7

Given PQ=2cm PQ = 2 \, \text{cm} and RS=2.5cm RS = 2.5 \, \text{cm} , to construct PQ+RS PQ + RS , measure PQ PQ using a compass. Place the compass point on P P' and draw an arc. Then, measure RS RS using the compass, place the compass point on the arc, and draw another arc. Draw a line segment PQ P'Q' through these points.

STEP 8

To construct 2×PQ 2 \times PQ , measure PQ PQ using a compass. Without changing the compass width, place the compass point on P P'' and mark an arc. Then, place the compass point on the arc and mark another arc. Draw a line segment PQ P''Q'' through these points.

STEP 9

To construct RSPQ RS - PQ , measure RS RS using a compass. Place the compass point on R R' and draw an arc. Measure PQ PQ using the compass, place the compass point on the arc, and mark another arc inside the first arc. Draw a line segment RS R'S' through these points.

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