6. Triangles

*नोट: यह सेक्शन रिवीजन के लिए है। अपना ज्ञान परखने के लिए ऊपर दिए गए क्विज़ में भाग लें।

1. Two polygons having the exact same number of sides are perfectly similar if their corresponding angles are equal and their corresponding sides are in what?
   A) Equal length  |  B) Same ratio  |  C) Different proportion  |  D) Opposite direction
2. All completely geometric circles drawn on a plane are mathematically always what?
   A) Congruent  |  B) Similar  |  C) Parallel  |  D) Equal
3. All perfectly uniform squares drawn geometrically are strictly always what?
   A) Congruent  |  B) Similar  |  C) Asymmetrical  |  D) Rectangular
4. Two distinct triangles are mathematically similar if their corresponding geometrical angles are exactly what?
   A) Equal  |  B) Unequal  |  C) Supplementary  |  D) Complementary
5. The famous Basic Proportionality Theorem is also universally known by which mathematical name?
   A) Pythagoras Theorem  |  B) Euler Theorem  |  C) Thales Theorem  |  D) Newton Theorem
6. If a line is strictly drawn parallel to one side of a triangle intersecting the other 2 sides, the other 2 sides divide in the exact same what?
   A) Area  |  B) Volume  |  C) Ratio  |  D) Perimeter
7. All perfectly equilateral triangles constructed on a plane are always strictly what?
   A) Congruent  |  B) Similar  |  C) Right angled  |  D) Isosceles only
8. To mathematically apply the AAA similarity criterion perfectly, exactly how many corresponding angles must strictly match?
   A) 1  |  B) 2  |  C) 3  |  D) 4
9. Which exact mathematical symbol is universally used to denote similarity between two distinct geometrical figures?
   A) =  |  B) ≅  |  C) ~  |  D) ≠
10. If two perfectly similar triangles are absolutely congruent to each other, what is the exact numerical ratio of their corresponding sides?
    A) 1:2  |  B) 2:1  |  C) 1:1  |  D) 3:1
11. In triangle ABC, D and E are exact points on AB and AC. If DE is perfectly parallel to BC, AD=2, DB=3, and AE=4, find exactly the length of AC.
    A) 6  |  B) 8  |  C) 10  |  D) 12
12. If triangle ABC is mathematically similar to triangle DEF, angle A=47 degrees and angle E=83 degrees, find exactly the measure of angle C.
    A) 40 degrees  |  B) 50 degrees  |  C) 60 degrees  |  D) 70 degrees
13. The absolute ratio of the corresponding sides of two perfectly similar triangles is exactly 4:9. What is the strictly mathematical ratio of their perimeters?
    A) 16:81  |  B) 2:3  |  C) 4:9  |  D) 8:27
14. A vertical pole exactly 6 m long directly casts a perfect shadow 4 m long. At the exact same time, a tall tower casts a continuous shadow 28 m long. Find the tower's exact mathematical height.
    A) 40 m  |  B) 42 m  |  C) 44 m  |  D) 46 m
15. In a distinct triangle PQR, if a straight line perfectly parallel to QR cuts PQ at exactly M and PR at exactly N, what is the mathematical ratio PM/MQ equal to?
    A) PR/NR  |  B) PN/NR  |  C) NR/PN  |  D) PQ/PR
16. If triangle ABC is similar to triangle PQR, AB = 3 cm, BC = 5 cm, CA = 6 cm, and PQ = 9 cm, find the exact mathematical length of side QR.
    A) 10 cm  |  B) 12 cm  |  C) 15 cm  |  D) 18 cm
17. If strictly in two distinct triangles ABC and PQR, the ratio AB/QR = BC/PR = CA/PQ mathematically holds true, then which similarity is perfectly correct?
    A) Triangle ABC ~ Triangle PQR  |  B) Triangle ABC ~ Triangle QRP  |  C) Triangle ABC ~ Triangle RQP  |  D) Triangle BCA ~ Triangle PQR
18. The direct geographical shadow of a 10m high building is exactly 15m. Find the strict mathematical height of a nearby tree that casts a 6m shadow simultaneously.
    A) 2m  |  B) 3m  |  C) 4m  |  D) 5m
19. In a mathematical trapezium ABCD, side AB is perfectly parallel to side DC. Their geometrical diagonals intersect exactly at O. If AB = 2DC, strictly find the linear ratio of AO to OC.
    A) 1:2  |  B) 2:1  |  C) 3:1  |  D) 1:3
20. Which of the following is absolutely not a valid mathematical criterion for directly proving the geometrical similarity of two distinct triangles?
    A) AAA  |  B) SSS  |  C) SAS  |  D) SSA
21. Let triangle ABC be perfectly similar to triangle DEF and their exact mathematical areas be 64 sq cm and 121 sq cm respectively. If EF = 15.4 cm, find the exact length of BC.
    A) 9.8 cm  |  B) 10.5 cm  |  C) 11.2 cm  |  D) 12.4 cm
22. The diagonals of a complete trapezium ABCD with AB parallel to DC intersect exactly at point O. If AB=2CD, find the exact mathematical ratio of the areas of triangles AOB and COD.
    A) 1:4  |  B) 2:1  |  C) 4:1  |  D) 8:1
23. In a specific triangle ABC, AD is completely perpendicular to BC and exactly AD^2 = BD x CD. Mathematically, what is the strictly exact measure of angle BAC?
    A) 45 degrees  |  B) 60 degrees  |  C) 90 degrees  |  D) 120 degrees
24. Two perfectly similar triangles mathematically have their corresponding geometric sides in the exact ratio of 2:3. What is the strict mathematical ratio of their vertical altitudes?
    A) 4:9  |  B) 2:3  |  C) 8:27  |  D) 16:81
25. Two distinct mathematically similar triangles have their corresponding internal medians in the exact numerical ratio 4:5. What is the strictly exact ratio of their corresponding total areas?
    A) 4:5  |  B) 8:10  |  C) 16:25  |  D) 64:125
26. If the exact mathematical ratio of the calculated areas of two perfectly similar triangles is 16:81, what is the absolute ratio of their corresponding geometrical angle bisectors?
    A) 2:3  |  B) 4:9  |  C) 16:81  |  D) 8:27
27. In a perfectly equilateral triangle ABC, exactly D is a point strictly on side BC such that BD = 1/3 BC. Find the exact mathematical ratio of AD^2 to AB^2.
    A) 5:9  |  B) 7:9  |  C) 8:9  |  D) 1:3
28. A street light bulb is strictly fixed 4.8 m above the level ground. A girl of exact height 1.2 m is walking away perfectly at 1.5 m/s. Find her exact shadow length mathematically after exactly 4 seconds.
    A) 1.2 m  |  B) 1.6 m  |  C) 2.0 m  |  D) 2.4 m
29. If triangle ABC is perfectly similar to triangle DEF, and their strict mathematical perimeters are 30 cm and 18 cm respectively. If exactly BC = 9 cm, mathematically find the precise length of EF.
    A) 4.8 cm  |  B) 5.4 cm  |  C) 6.0 cm  |  D) 7.2 cm
30. In a perfect geometrical right-angled triangle, if a perpendicular is strictly drawn from the exact right angle vertex directly to the hypotenuse, the two formed triangles are mathematically what?
    A) Congruent to each other  |  B) Similar to the whole triangle  |  C) Equal in area  |  D) Equilateral in shape