Geometry Class 10 Quiz

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Questions and Answers

If triangles Δ ABC and Δ PQR are similar, and AB = 4 cm, PQ = 6 cm, QR = 9 cm, what is the length of BC?

6 cm

7 cm

9 cm

8 cm (correct)

What is the measure of the arc length for arc PRQ if ∠PRQ is 75°?

75°

210°

285°

150° (correct)

Given the point A(1, 3) on a vertical line, which of the following could be the coordinates of point B?

(1, -3)

(5, 3) (correct)

(3, 1)

(3, 0)

Which set of numbers does not form a Pythagorean triplet?

(12, 9, 15) Signup and view all the answers

If AB || BC and DC || BC with lengths AB = 3 and DC = 4, what is the ratio of area A(ΔABC) to A(ADCB)?

3:4 Signup and view all the answers

What is the side length of a square whose diagonal measures $12 oot{2}$ cm?

6 cm Signup and view all the answers

If tan θ = $\sqrt{3}$, what is the value of θ?

60° Signup and view all the answers

In a circle with radius 6 cm, if line AB is tangent at point A, what is the measure of ∠CAB?

90° Signup and view all the answers

What is the length of segment EF in triangle DEF if DE = 33 cm and DF = 65 cm?

58 cm Signup and view all the answers

If the measure of two arcs of a circle are 2x and 7x degrees, what is the measure of the minor arc?

5x Signup and view all the answers

What is the sum of coordinates for the centroid of triangle ABC with vertices A(-7, 6), B(2, 2), and C(8, 5)?

14/3 Signup and view all the answers

If sin θ = 7/25, what is the approximate value of cos θ?

24/25 Signup and view all the answers

In similar triangles Δ ABC and Δ PQR, if the ratio of the areas is 81:121, what is the ratio of the corresponding side lengths?

9:11 Signup and view all the answers

In the context of circles touching at point Z, what conclusion can be drawn about segments XA and YB?

They are parallel. Signup and view all the answers

For a cyclic quadrilateral ABCD where AB = AD and ∠BCD = 70°, what is the measure of arc BCD?

140° Signup and view all the answers

In Δ LMN and Δ LQP where Δ LMN is similar to Δ LQP, if LM = 3.6 cm and LN = 4.2 cm, what can be inferred about LQ?

LQ = 7 cm Signup and view all the answers

Signup and view all the answers

Study Notes

Instructions & Information

All questions are compulsory
Calculators are not allowed
Only the first attempt for multiple choice questions (MCQs) is graded
The correct answer alternative (A, B, C, or D) for MCQs, along with the sub-question number, is required
Draw figures when needed
Construction marks must be clear and not erased
Diagrams are essential for proving theorems

Multiple Choice Questions (MCQ)

Δ ABC ~ Δ PQR ; if AB = 4 cm, PQ = 6 cm, and QR = 9 cm, then BC = 6 cm
∠PRQ is inscribed in arc PRQ of a circle with center O. If ∠PRQ = 75°, then arc PRQ = 150°
Seg AB is parallel to the Y-axis and the coordinates of point A are (1, 3). The coordinates of point B can be (1, -3)
The Pythagorean triplet that is NOT a Pythagorean triplet is (12, 9, 15)

Sub-Questions (B)

In a figure, given AB ⊥ BC and DC ⊥ BC. If AB = 3 and DC = 4, find the ratio of areas A(ΔABC) / A(ΔDCB)
Given the diagonal of a square is 12√2 cm, find the side length
Given tan θ = √3, find the value of θ
Given a circle with center C and radius 6 cm. Line AB is a tangent at point A. Find the measure of ∠CAB.

(Note: Further sub-questions are given for different problems)

Complete the Following Activity (A)

In Δ ABC, line PQ is parallel to BC. If AP = 10, PB = 12, and AQ = 15,then find QC. The activity shows calculations to find QC. The result is QC = 18cm.

Find ∠AOB and ∠ACB

In a circle with center O, chord AB is equal to the radius of the circle. ∠AOB = ? (Answer: 60°) and ∠ACB = ? (Answer: 30°)

Distance between Points

Find the distance between points P(6, -6) and Q(3, -7). The solution method utilizes the distance formula. The answer is √13.

Additional Sub-Questions

Find EF in Δ DEF, where ∠E = 90°, DE = 33 cm, and DF = 65 cm.
Two arcs formed by a chord of a circle have measures 2x and 7x degrees. Find the measure of the minor arc.
Find the coordinates of the centroid for triangle ABC given vertices: A(-7, 6), B(2, 2), and C(8, 5).
If sin θ = 7/25, find the value of cos θ

Prove That...

In a right-angled triangle, the perpendicular segment to the hypotenuse from the opposite vertex is the geometric mean of the segments into which the hypotenuse is divided.
Cyclic quadrilateral ABCD; AB = AD, and ∠BCD = 70°. Find: m(arc BCD), m(arc BAD), and ∠ABD.

Additional Geometry Problems

(Geometry problems are listed, including specific figures and constructions)

Circle with Centre P

Draw a circle with center P and radius 3.5 cm.
Draw an arc AB of 120° measure.
Draw tangents to the circle at points A and B.

Prove that...

1 - cos A / √1 + cos A = cosec A - cot A.
Given consecutive angles of a cyclic quadrilateral are congruent, prove that one pair of opposite sides is parallel and the other pair is congruent.
Δ LMN ~ Δ LQP. Provide given values and construct the triangles.
In Δ PQR, seg XY || side QR, M and N are midpoints of PY and PR. Prove seg XM || seg QN and ΔPXM ≅ ΔPQN.

Angle Bisector and Circle

Draw angle ABC of 65°.
Draw ray BM which bisects angle B.
Take point P on BM such that BP = 4 cm.
Draw perpendicular from P to BC.
Draw a circle with center P and radius equal to the perpendicular length.
Determine the relation of the circle to the angle's arms.
Given A(2, 1) and B(-3, 6) & ratio 2:3, determine if point P lies on the line x - 5y + 15 = 0.

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Description

Test your knowledge of geometry concepts with this comprehensive quiz. Covering similarity of triangles, angles inscribed in circles, coordinate geometry, and Pythagorean triplets, this quiz is designed for 10th-grade students. Make sure to draw diagrams where necessary and only utilize your first attempt for grading!