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ExampleThe bisectors of two angles on the same side of a parallelogram cut each other at right angles.

### ExampleThe bisectors of two angles on the same side of a parallelogram cut each other at right angles.

1. Prove that a rilateral is a parallelogram if its(a) opposite angles are congruent.

### 1. Prove that a rilateral is a parallelogram if its(a) opposite angles are congruent.

2. Take a line segment of length 5.5 \mathrm{~cm} and divide it into five congruent parts.[Hint: Draw an acute angle \angle \mathrm{BAX} . On \overline{\mathrm{AX}} take \overline{\mathrm{AP}} \cong \overline{\mathrm{PQ}} \cong \overline{\mathrm{QR}} \cong \overline{\mathrm{RS}} \cong \overline{\mathrm{ST}} .

### 2. Take a line segment of length 5.5 \mathrm{~cm} and divide it into five congruent parts.[Hint: Draw an acute angle \angle \mathrm{BAX} . On \overline{\mathrm{AX}} take \overline{\mathrm{AP}} \cong \overline{\mathrm{PQ}} \cong \overline{\mathrm{QR}} \cong \overline{\mathrm{RS}} \cong \overline{\mathrm{ST}} .

2. In parallelogram A B C D (i) \mathrm{m} \overline{\mathrm{AB}}

### 2. In parallelogram A B C D (i) \mathrm{m} \overline{\mathrm{AB}}

2. In parallelogram A B C D (ii) \mathrm{m} \overline{\mathrm{BC}} \ldots \ldots \mathrm{m} \overline{\mathrm{AD}}

### 2. In parallelogram A B C D (ii) \mathrm{m} \overline{\mathrm{BC}} \ldots \ldots \mathrm{m} \overline{\mathrm{AD}}

1. Prove that a rilateral is a parallelogram if its(b) diagonals bisect each other.

### 1. Prove that a rilateral is a parallelogram if its(b) diagonals bisect each other.

6. In the question 5 sum of the opposite angles of the parallelogram is 110^{\circ} find the remaining angles.

### 6. In the question 5 sum of the opposite angles of the parallelogram is 110^{\circ} find the remaining angles.

4. If the given figure \mathrm{ABCD} is a parallelogram then find x m .

### 4. If the given figure \mathrm{ABCD} is a parallelogram then find x m .

1. Fill in the blanks.(i) In a parallelogram opposite sides are(ii) In a parallelogram opposite angles are(iii) Diagonals of a parallelogram each other at a point.(iv) Medians of a triangle are.(v) Diagonal of a parallelogram divides the parallelogram into two triangles.

### 1. Fill in the blanks.(i) In a parallelogram opposite sides are(ii) In a parallelogram opposite angles are(iii) Diagonals of a parallelogram each other at a point.(iv) Medians of a triangle are.(v) Diagonal of a parallelogram divides the parallelogram into two triangles.

1. In the given figure \overleftrightarrow{\mathrm{AX}}\|\overleftrightarrow{\mathrm{BY}}\| \overleftrightarrow{\mathrm{CZ}} \| \stackrel{\leftrightarrow}{\mathrm{DU} \| \mathrm{EV}} and \overline{\mathrm{AB}} \cong \overline{\mathrm{BC}} \cong \overline{\mathrm{CD}} \cong \overline{\mathrm{DE}} .If \mathrm{mMN}=1 \mathrm{~cm} then find the length of \overline{\mathrm{LN}} and \overline{\mathrm{LQ}} .

### 1. In the given figure \overleftrightarrow{\mathrm{AX}}\|\overleftrightarrow{\mathrm{BY}}\| \overleftrightarrow{\mathrm{CZ}} \| \stackrel{\leftrightarrow}{\mathrm{DU} \| \mathrm{EV}} and \overline{\mathrm{AB}} \cong \overline{\mathrm{BC}} \cong \overline{\mathrm{CD}} \cong \overline{\mathrm{DE}} .If \mathrm{mMN}=1 \mathrm{~cm} then find the length of \overline{\mathrm{LN}} and \overline{\mathrm{LQ}} .

1. Prove that the line-segments joining the mid-points of the opposite sides of a rilateral bisect each other.

### 1. Prove that the line-segments joining the mid-points of the opposite sides of a rilateral bisect each other.

3. Prove that the line-segment passing through the mid-point of one side and parallel to another side of a triangle also bisects the third side.

### 3. Prove that the line-segment passing through the mid-point of one side and parallel to another side of a triangle also bisects the third side.

1. One angle of a parallelogram is 130^{\circ} . Find the measures of its remaining angles.

### 1. One angle of a parallelogram is 130^{\circ} . Find the measures of its remaining angles.

2. Prove that the line-segments joining the mid-points of the opposite sides of a rectangle are the right-bisectors of each other.[Hint: Diagonals of a rectangle are congruent.]

### 2. Prove that the line-segments joining the mid-points of the opposite sides of a rectangle are the right-bisectors of each other.[Hint: Diagonals of a rectangle are congruent.]

2. Prove that a rilateral is a parallelogram if its opposite sides are congruent.

### 2. Prove that a rilateral is a parallelogram if its opposite sides are congruent.

2. In parallelogram A B C D (iii) \mathrm{m} \angle 1 \cong \ldots \ldots

### 2. In parallelogram A B C D (iii) \mathrm{m} \angle 1 \cong \ldots \ldots

1. The distances of the point of concurrency of the medians of a triangle from its vertices are respectively 1.2 \mathrm{~cm} 1.4 \mathrm{~cm} and 1.6 \mathrm{~cm} . Find the lengths of its medians.

### 1. The distances of the point of concurrency of the medians of a triangle from its vertices are respectively 1.2 \mathrm{~cm} 1.4 \mathrm{~cm} and 1.6 \mathrm{~cm} . Find the lengths of its medians.

5. The given figure LMNP is a parallelogram. Find the value of m n .

### 5. The given figure LMNP is a parallelogram. Find the value of m n .

2. Prove that the point of concurrency of the medians of a triangle and the triangle which is made by joining the mid-points of its sides is the same.

### 2. Prove that the point of concurrency of the medians of a triangle and the triangle which is made by joining the mid-points of its sides is the same.

2. One exterior angle formed on producing one side of a parallelogram is 40^{\circ} Find the measures of its interior angles.