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What is the sum of all the angles of a triangle?

In a parallelogram the sum of two consecutive angles is

Factorise:
$(x+2{)}^3+(x-2{)}^3$

Match the following table:

$\begin{array}{cc}\text{Theorem Statement}& \text{Theorem Name}\\ \text{(a) The line segment joining the mid-points of}& \text{(i) Basics proportionality theorem}\\ \text{two sides of a triangle is parallel to the third side}& \\ \text{(b) A line parallel to one side of a triangle divides}& \text{(ii) Mid point theorem}\\ \text{the other two sides into parts of equal}& \\ \text{poportion}& \\ \text{(c) If a line divides the any tw o sides of a triangle}& \text{(iii) Converse of Basic porpotionality theorem}\\ \text{in the same ratio, then the line must be parallel}& \\ \text{to the third side.}& \end{array}$

What is the area of the rhombus ABCD below, if AC=12cm and BE= 16cm.

In ΔABC and ΔDEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see the given figure). Show that

(i) Quadrilateral ABED is a parallelogram

(ii) Quadrilateral BEFC is a parallelogram

(iii) AD || CF and AD = CF

(iv) Quadrilateral ACFD is a parallelogram

(v) AC = DF

(vi) ΔABC ≅ ΔDEF.

Question 6

In $\Delta ABC$, if L and M are the points on AB and AC, respectively such that LM || BC. Prove that $ar\left(\Delta LOB\right)=ar\left(\Delta MOC\right)$.

In Fig. BM and DN are both perpendiculars to the segments AC and BM = DN. Prove that AC bisects BD [3 MARKS]

A parallelogram whose all sides are equal is called a _____.

Question 4

A football player scored the following number of goals in the 10 matches.

1, 3, 2, 5, 8, 6, 1, 4, 7 and 9.

Since the number of matches is 10 ( an even number),

$\text{Median}=\frac{\text{5th observation + 6th observation}}{2}=\frac{8+6}{2}=7$

Is it the correct answer and why?

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{17}{8}$

The hypotenuse of a right angled triangle is $25cm.$ The other two sides are such that one is $5cm$ longer than the other. Their lengths (in cm) are

In a fair, there is a shop with gifts. You have to throw two dice at once (they are not identical). Before throwing, you have to predict the sum of the face values of the two dice. If you get the sum as predicted, you will get a free gift. Which number has the maximum chance of getting you the gift?

Find the value of x, y and z in the figure given below.

The median of a triangle divided it into two

(a) triangles of equal area

(b) congruent traingles

(c) isosceles triangles

(d) right triangles

From the middle of a square, a small square is cut off. The area of the resulting figure is 65 square centimetres and the sum of the lengths of all its edges is 52 centimetres. What is the length of a side of the original square and the square cut off?

Find the Y intercept of 2x - 3y = -6

Write the rationalisation factor of $7-3\sqrt{5}$.

Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or a non-terminating decimal expansion:

$\frac{7^3}{2^3\times 5^2}$ and $\frac{3\times 7^3}{2^3\times 3}$

Expand the given expression using identitites:

${(a^2-b^2)}^2$

In the given figure, R is an external point and RP and RQ are tangents drawn to the circle from R. $\angle POQis{90}^{\circ }$. The quadrilateral OPRQ is a ____and the $\angle$ POR is ___

Question 2(a)

Out of 30 students in a class, 6 like football, 12 like cricket and remaining like tennis. Find the ratio of:

The number of students liking football to the number of students liking tennis.

Each edge of a cube is increased by $50\%$, then percentage increase in its surface area =.

Given that AB || CD, intersected by a transversal. ∠1 = (120 - x)^o and ∠5 = 5x^o, then the measures of ∠1 and ∠5 are