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Solved Examples
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e   Given a regular hexagon with one of its base as 8 cm, it was cut into co-triangles with center O. What is the sum of the length of all the midsegments of all the triangles?   e View Solution
e   Vertex of a kite are (3, 0), (0, 4), (- 3, 0) and (0, - 8). The mid points of the sides of the kite are joined to form a quadrilateral. Find the area of the quadrilateral.
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e   Find the value of z from the figure.
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e   Which of the following is/are correct?
1. Line joining the midpoints of the sides of a square form a square.
2. Line joining the midpoints of the sides of a rhombus form a rhombus.
3. Line joining the midpoints of the sides of a parallelogram form a parallelogram.
4. Line joining the midpoints of the sides of a rectangle form a rectangle.
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e   Find the value of (x² + 2).
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e   XY¯ is the length of the midsegment drawn for the two triangles. Find the length of FY¯.
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e   Find the length of midsegment EF¯.
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e   Find the value of DE¯.
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e   In the figure, AD¯ is the median of ΔABC. BE : ED = 2 : 3. P is the midpoint of AB¯ and PQ¯ || BC¯. Find the length of PQ¯.   e View Solution
e   Which of the following statements are correct?
1. If BC¯ || DE¯, then D and E are the midpoints of AB¯ and AC¯.
2. If the length of BC¯ is twice the length of DE¯, then D and E are the midpoints of AB¯ and AC¯.
3. If D is the midpoint of AB¯ and DE¯ || BC¯, then E is the midpoint of AC¯.   e
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e   AB¯ || DE¯. D is the midpoint of AC¯. Find the coordinates of D and E.
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e   Find the point F from the figure if AB¯ || GH¯.   e View Solution
e   The length of one diagonal of a rhombus is twice the other. Area of the rectangle obtained by joining the midpoints of the sides of the rhombus is 18 units. Find the length of the longer diagonal.   e View Solution
e   Find the value of x from the figure.
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e   Find the value of x from the given figure.   e View Solution
e   What type of triangle is formed by joining the midsegments of an equilateral triangle?   e View Solution
e   Find the value of x from the figure.   e View Solution
e   Find the value of x from the figure.
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e   Find the values of x and y from the following equilateral triangle.   e View Solution
e   In the given triangle if FG¯ is midsegment of ΔAED and DE¯ is the midsegment of ΔACB, then find the value of x.
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e   If x is the length of MN¯ which is the midsegment of ΔABC, then find the value of BC¯.   e View Solution
e   Given a regular hexagon with one of its base as 4 cm, it was cut into co-triangles with center O. What is the sum of the length of all the midsegments of all the triangles?   e View Solution
e   The length of the diagonal of a square is 12 in. Two diagonals intersect to form four congruent triangles. Find the length of the mid-segment of any triangle parallel to the side of the square.   e View Solution
e   Find the value of x from the figure if OC = CE and OD = DF.   e View Solution
e   Find the values of x and y from the given figure.
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e   ABCD is a rhombus. E, F, G and H are the mid points of the sides.What can you say about the area of EFGH?   e View Solution
e   ABCD is a quadrilateral. P, Q, R and S are the mid points of sides AB¯, BC¯, CD¯ and DA¯ respectively. What is the best description of PQRS?   e View Solution
e   ABCD is a quadrilateral with vertices A(0, 0), B(4, 1), C(6, 8) and D(0, 3). P, Q, R and S are the midpoints of AB¯, BC¯, CD¯ and DA¯ respectively. Find the perimeter of PQRS.
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