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In the figure, AB, PQ and CD are parallel to each other. Prove that 1/x + 1/y = 1/z. Triangles.
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In the figure, AB, PQ and CD are parallel to each other. AB = x units, CD = y units and PQ = z units. Prove that 1/x + 1/y = 1/z
TRIANGLES CLASS 10 IMPORTANT QUESTIONS.
triangles class 10 important questions
Here are some of the important questions from outside the NCERT with their links as well:
1) In the figure, AB, PQ and CD are parallel to each other. AB = x units, CD = y units and PQ = z units. Prove that 1/x + 1/y = 1/z.
2) ABC is a right triangle, right angled at C. If p is the length of the perpendicular from C to AB and AB = c, BC = a and CA = b, then prove that 1/p^2 = 1/a^2 + 1/b^2
3) In the figure DEFG is a square. angle BAC = 90. Prove that DE^2 = BD x EC.
4) If A is the area of a right angled triangle and b is one of the sides containing the right angle, prove that the length of the altitude on the hypotenuse is 2Ab/ square root of (b^4 + 4A^2)
5) In the given figure, M is the mid point of side CD of a parallelogram ABCD. The line BM is drawn intersecting AC at L and AD produced at E. Prove that EL=2BL
6) In the figure S and T trisect the side QR of a right triangle PQR. Prove that 8PT^2 = 3 PR^2 + 5 PS^2
7) In triangle ABC, P and Q are points on AB and AC such that PQ is parallel to BC. Prove that median AD bisects PQ.
8) Prove that three times the sum of squares of sides of a triangle is equal to four times the sum of the squares of its medians.
9)OB is the perpendicular bisector of the line segment DE. FA is perpendicular to OB and FE intersects OB at point C. Prove that 1/OA+1/OB=2/OC.
10) The side BC of a triangle ABC is bisected at D. O is any point on AD. BO and CO produced meet AC and AB at E and F respectively. AD is produced to X so that D is the mid point of OX. Show that FE is parallel to BC.
TRIANGLES CLASS 10 IMPORTANT QUESTIONS.
triangles class 10 important questions
Here are some of the important questions from outside the NCERT with their links as well:
1) In the figure, AB, PQ and CD are parallel to each other. AB = x units, CD = y units and PQ = z units. Prove that 1/x + 1/y = 1/z.
2) ABC is a right triangle, right angled at C. If p is the length of the perpendicular from C to AB and AB = c, BC = a and CA = b, then prove that 1/p^2 = 1/a^2 + 1/b^2
3) In the figure DEFG is a square. angle BAC = 90. Prove that DE^2 = BD x EC.
4) If A is the area of a right angled triangle and b is one of the sides containing the right angle, prove that the length of the altitude on the hypotenuse is 2Ab/ square root of (b^4 + 4A^2)
5) In the given figure, M is the mid point of side CD of a parallelogram ABCD. The line BM is drawn intersecting AC at L and AD produced at E. Prove that EL=2BL
6) In the figure S and T trisect the side QR of a right triangle PQR. Prove that 8PT^2 = 3 PR^2 + 5 PS^2
7) In triangle ABC, P and Q are points on AB and AC such that PQ is parallel to BC. Prove that median AD bisects PQ.
8) Prove that three times the sum of squares of sides of a triangle is equal to four times the sum of the squares of its medians.
9)OB is the perpendicular bisector of the line segment DE. FA is perpendicular to OB and FE intersects OB at point C. Prove that 1/OA+1/OB=2/OC.
10) The side BC of a triangle ABC is bisected at D. O is any point on AD. BO and CO produced meet AC and AB at E and F respectively. AD is produced to X so that D is the mid point of OX. Show that FE is parallel to BC.
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