Today our topic of discussion is Area Related Theorems and Constructions Exercises 15.
Area Related Theorems and Constructions Exercises 15
Exercise 15
- The lengths of three sides of a triangle are given, in which case below the construction of a right-angled triangle is not possible?
1) 3 cm, 4 cm, 5 cm
2) 6 cm, 8 cm, 10 cm
3) 5 cm, 7 cm, 9 cm
4) 5 cm, 12 cm, 13 cm
- In plane geometry:
(1) Each of the bounded plane has definite area.
(ii) If the area of two triangles is equal, the two triangles are congruent.
(iii) If the two triangles are congruent, their area is equal.
Which one of the following is correct?
1) i and ii
2) i and iii
3) ii and iii
4) i, ii and iii
In the adjacent figure, AABC is equilateral, AD 1 BC and AB = 2 Based on the information mentioned above,
answer question no. 3 and 4:
- BD what?
1) 1
2) √2
3) √3
4) 4
- What is the height of the triangle?
1) 4/√3
2) √3
3) 2/√3
4) 2√3
- Prove that, the diagonals of a parallelogram divide the parallelogram into four equal triangular regions.
- Prove that, the area of a square is half the area of the square drawn on its diagonal.
- Prove that, any median of a triangle divides the triangular region into two regions of equal area.
- A parallelogram and a rectangular region of equal area lie on the same side of the bases. Show that, the perimeter of the parallelogram is greater than that of the rectangle.
- X and Y are the mid points of the sides AB and AC of ΔABC . Prove that the area of triangle AXY = 1/4 * C area of the triangular region ΔABC .
- ABCD is a trapezium. The sides AB and CD are parallel to each other. Find the area of the region bounded by the trapezium ABCD.
- P is any point interior to the parallelogram ABCD. Prove that the area of ΔPAB + the area of ΔPCD= 1 2 ( areac the parallelogram ABCD).
- A line parallel to base BC of the ΔABC intersects AB and AC at D and E respectively. Prove that, ΔDBC = ΔEBC and ΔDBF = ΔCDE.
- angle A = 1 right angle of the triangle ABC. D is a point on AC. Prove that
B * C ² + A * D ² = B * D ² + A * C²
- ABC is an isosceles right triangle. BC is its hypotenuse and P is any point on BC. Prove that P * B² + P * C² = 2P * A²
- angle C is an obtuse angle of triangle ABC AD is perpendicular to BC. Show that
A * B ^ 2 = A * C²+ B * C²+ 2BCCD
- ZC is an acute angle of triangle ABC ; AD is perpendicular to BC. Show that A * B² = A * C² + B * C² – 2BCCD
- QD is a median of the triangle PQR .
1) Draw a proportional figure according to the stem.
2) Prove that, P * Q² + Q * R²= 2(P * D² + Q * D ²)
3) If PQ = QR = PR then prove that, 4Q * D²= 3P * Q²
- ABCD is a parallelogram where AB = 5cm ,AD =4 cm and ∠BAD = 75 ° APML is another parallelogram where ∠LAP = 60 °. Area of ΔAED and area of parallelogram APML are equal to the area of parallelogram ABCD.
1) Draw ∠BAD by using pencil, compass and scale.
2) Draw ΔAED [drawing and description are must].
3) Draw parallelogram APML [drawing and description are must].
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