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Show that A(1, 2), B(4, 3), C(6, 6) and D(3, 5) are the vertices of a Parallelogram. Show that ABCD is not a rectangle.
In figure 3.94,
(1) m(arc CE) = 54°,
m(arc BD) = 23°, find measure of ∠CAE.
(2) If AB = 4.2, BC = 5.4,
AE = 12.0, find AD
(3) If AB = 3.6, AC = 9.0,
AD = 5.4, find AE
(1) m(arc CE) = 54°,
m(arc BD) = 23°, find measure of ∠CAE.
(2) If AB = 4.2, BC = 5.4,
AE = 12.0, find AD
(3) If AB = 3.6, AC = 9.0,
AD = 5.4, find AE
Write another proof of the above theorem (property of an angle bisector of a triangle). Use the following properties and write the proof.
i. The areas of two triangles of equal height are proportional to their bases.
ii. Every point on the bisector of an angle is equidistant from the sides of the angle.
Given: In $\triangle CAB$,ray AD bisects ∠A.
To prove: $\frac{A B}{A C}=\frac{B D}{D C}$
Construction: Draw seg DM ⊥ seg AB A – M – B and seg DN ⊥ seg AC, A – N – C.
→i. The areas of two triangles of equal height are proportional to their bases.
ii. Every point on the bisector of an angle is equidistant from the sides of the angle.
Given: In $\triangle CAB$,ray AD bisects ∠A.
To prove: $\frac{A B}{A C}=\frac{B D}{D C}$
Construction: Draw seg DM ⊥ seg AB A – M – B and seg DN ⊥ seg AC, A – N – C.
Express the following as a fraction in simplest form:
$0.\bar8$
→$0.\bar8$
If $\theta=30^\circ,$ verify that.
$\sin2\theta=\frac{2\tan\theta}{1+\tan^2\theta}$
→$\sin2\theta=\frac{2\tan\theta}{1+\tan^2\theta}$
Find the largest number which divides 615 and 963 leaving remainder 6 in each case.
A solid metallic sphere of diameter 28cm is melted and recast into a number of smaller cones, each of diameter 4cm and height 3cm. Find the number of cones so formed.
Solve the following system of equations by the method of cross-multiplication:
ax + by = a - b,
bx - ay = a + b.
$\square ABCD$ is a trapezium in which $AB \| DC$ and its diagonals intersect each other at point $O$. Show that $A O: B O=C O: D O$.
→The following table gives the distribution of total household expenditure (in rupee) of workers in a city.
Find the mean expenses per household by step deviation method.
| Expenditure (in rupees) | 100-150 | 150-200 | 200-250 | 250-300 | 300-350 | 350-400 | 400-450 |
| No. of workers | 24 | 40 | 33 | 28 | 30 | 22 | 16 |