Maths 4 Marks Questions

1. Points are A, B, C, D, P and R.

2. $\overline{\text{EF}},\ \overline{\text{GH}},\ \overline{\text{FH}},\ \overline{\text{EG}},\ \overline{\text{MN}}$

3. $\overrightarrow{\text{EP}},\ \overrightarrow{\text{GR}},\ \overrightarrow{\text{HS}},\ \overrightarrow{\text{FQ}}$

4. $\overleftrightarrow{\text{AB}},\ \overleftrightarrow{\text{CD}},\ \overleftrightarrow{\text{PQ}},\ \overleftrightarrow{\text{RS}}$

5. Collinear points are M, E, G and B.

1. Two pairs of intersecting lines and their point of intersection are.

$\bigg\{\overleftrightarrow{\text{EF}},\ \overleftrightarrow{\text{GH}},\ \text{point}\text{ R}\bigg\},\bigg\{\overleftrightarrow{\text{AB}},\ \overleftrightarrow{\text{CD}},\ \text{point}\text{ P}\bigg\}$

2. Three concurrent lines are.

$\bigg\{\overleftrightarrow{\text{AB}},\ \overleftrightarrow{\text{EF}},\ \overleftrightarrow{\text{GH}},\ \text{point}\text{ R}\bigg\}$

3. Three rays are.

$\bigg\{\overrightarrow{\text{RB}},\ \overrightarrow{\text{RH}},\ \overrightarrow{\text{RF}}\bigg\}$

4.  Two line segments are.

$\Big\{\overline{\text{RQ}}\text{ and }\overline{\text{RP}}\Big\}$

1. It is given that L is the mid-point of AB.

$\therefore\text{AL}=\text{BL}=\frac{1}{2}\text{AB}\ .....(1)$

Also, M is the mid-point of BC.

$\therefore\text{BM}=\text{MC}=\frac{1}{2}\text{BC}\ .....(2)$

$\text{AB}=\text{BC}$ (Given)

$\Rightarrow\frac{1}{2}\text{AB}=\frac{1}{2}\text{BC}$ (Things which are halves of the same thing are equal to one another)

$\text{AL}=\text{MC}$ [From (1) and (2)]

2. It is given that L is the mid-point of AB.

$\therefore\text{AL}=\text{BL}=\frac{1}{2}\text{AB}$

$\Rightarrow2\text{AL}=2\text{BL}=\text{AB}\ .....(3)$

Also, M is the mid-point of BC.

$\therefore\text{BM}=\text{MC}=\frac{1}{2}\text{BC}$

$\Rightarrow2\text{BM}=2\text{MC}=\text{BC}\ .....(4)$

$\text{BL}=\text{BM}$ (Given)

$\Rightarrow2\text{BL}=2\text{BM}$ (Things which are double of the same thing are equal to one another)

$\Rightarrow\text{AB}=\text{BC}$ [From (3) and (4)]