Question 1

Q1: List all the linear pairs and vertically opposite angles you observe in Fig. 5.3: Linear Pairs$\angle a$ and $\angle b, \ldots$ Pairs of Vertically Op...

Accepted Answer

Given: Two lines intersecting, forming four angles labeled a, b, c, and d in a clockwise or counter-clockwise manner. To Find: All linear pairs and pairs of vertically opposite angles. Solution: Linear Pairs: A linear pair consists of two adjacent angles whose non-common sides are opposite rays. The...

Question 2

Q1: Draw some lines perpendicular to the lines given on the dot paper in Fig. 5.10.

Accepted Answer

To Do: Draw lines perpendicular to given lines on a dot paper. Method: A perpendicular line forms a right angle ($90^\circ$) with the original line. On a dot paper, we can use the grid of dots to draw perpendicular lines. 1.  For a horizontal line: A perpendicular line will be a vertical line. We ca...

Question 3

Q2: In Fig. 5.11, mark the parallel lines using the notation given above (single arrow, double arrow etc.). Mark the angle between perpendicular lines wit...

Accepted Answer

Given: A figure containing various lines and shapes. To Do: Identify and mark parallel and perpendicular lines. Solution: (a) How to spot perpendicular lines: Perpendicular lines are lines that intersect at a right angle ($90^\circ$). - Visually, they form a perfect 'L' or 'T' shape at their interse...

Question 4

Q3: In the dot paper following, draw different sets of parallel lines. The line segments can be of different lengths but should have dots as endpoints.

Accepted Answer

To Do: Draw different sets of parallel lines on dot paper. Method: To draw parallel lines on a dot paper, we can use the concept of slope or 'rise over run'. Parallel lines have the same slope. 1.  Draw the first line segment: Connect any two dots on the paper. Let's say this line goes 'a' units hor...

Question 5

Q4: Using your sense of how parallel lines look, try to draw lines parallel to the line segments on this dot paper. (a) Did you find it challenging to dra...

Accepted Answer

To Do: Draw lines parallel to given segments on dot paper using intuition. Solution: (a) Did you find it challenging to draw some of them? Yes, it can be challenging to draw parallel lines for segments that have a complex slope (e.g., moving 3 units right and 4 units up), especially when relying onl...

Question 6

Q5: In Fig. 5.13, which line is parallel to line a - line b or line c? How do you decide this?

Accepted Answer

Given: A figure showing three lines: line 'a', line 'b', and line 'c'. Line 'b' appears to maintain a constant distance from line 'a', while line 'c' appears to converge towards line 'a'. To Find: Which line ('b' or 'c') is parallel to line 'a' and the reason for it. Solution: Line b is parallel to...

Question 7

Q1: Can you draw a line parallel to l, that goes through point A? How will you do it with the tools from your geometry box? Describe your method.

Accepted Answer

To Construct: A line parallel to a given line 'l' and passing through a given external point 'A'. Tools: Ruler and set square. Method using a Ruler and Set Square: 1.  Step 1: Place the ruler along the given line 'l'. 2.  Step 2: Place one of the edges of the set square (the one that forms a right a...

Question 8

Q1: Find the angles marked below.

Accepted Answer

To Find: The value of the marked angles in each figure. (a) Given: Two parallel lines are intersected by a transversal. An angle is given as $60^\circ$. We need to find angle 'a'. Solution: Angle 'a' and the given $60^\circ$ angle are in corresponding positions. Since the lines are parallel, corresp...

Question 9

Q2: Find the angle represented by a.

Accepted Answer

Given: Two sets of parallel lines intersecting each other. Two angles, $60^\circ$ and $70^\circ$, are given at two of the intersection points. We need to find angle 'a'. Solution: Let's extend the lines forming the angle 'a' to form a triangle with the other given lines. 1.  The angle given as $70^\...

Question 10

Q3: In the figures below, what angles do x and y stand for?

Accepted Answer

To Find: The values of x and y in each figure. Figure 1 (Left): Given: Two parallel lines are intersected by a transversal. An angle is given as $130^\circ$. We need to find angles x and y. Solution: - The angle given as $130^\circ$ and angle 'x' are alternate exterior angles. Since the lines are pa...

Question 11

Q4: In Fig. 5.33, $\angle \mathrm{ABC}=45^{\circ}$ and $\angle \mathrm{IKJ}=78^{\circ}$. Find angles $\angle \mathrm{GEH}, \angle \mathrm{HEF}$, $\angle \...

Accepted Answer

Given: - Three parallel horizontal lines: AB || DE || IJ. - Three parallel slanted lines: AC || GH || IK. - $\angle ABC = 45^\circ$. - $\angle IKJ = 78^\circ$. To Find: $\angle GEH$, $\angle HEF$, $\angle FED$. Solution: 1.  Finding $\angle GEH$:     - The lines forming $\angle GEH$ are GE (which is...

Question 12

Q5: In Fig. 5.34, $A B$ is parallel to CD and CD is parallel to EF . Also, EA is perpendicular to AB . If $\angle \mathrm{BEF}=55^{\circ}$, find the value...

Accepted Answer

Given: - AB || CD || EF. - EA ⊥ AB, which means $\angle EAB = 90^\circ$. - $\angle BEF = 55^\circ$. - Angle 'x' is $\angle AEB$. - Angle 'y' is $\angle BCD$. To Find: The values of x and y. Solution: 1.  Finding x:     - Since AB || EF and AE is a transversal, the sum of the interior angles on the s...

Question 13

Q6: What is the measure of angle $\angle \mathrm{NOP}$ in Fig. 5.35? [Hint: Draw lines parallel to LM and PQ through points N and O.]

Accepted Answer

Given: - Line LM is parallel to line PQ (LM || PQ). - A zigzag line connects M to N, N to O, and O to Q. - $\angle LMN = 25^\circ$. - $\angle PQO = 45^\circ$. - Assuming the question asks for $\angle NOQ$ as P is a point on the line PQ. To Find: The measure of $\angle NOQ$. Solution: Let's use the h...

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