Triangles Important Questions.

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1. Q1Easy

   Which of the following is a valid similarity criterion for two triangles?

   • A.SSA (Side-Side-Angle)
   • B.AAA (Angle-Angle-Angle)
   • C.SAS (Side-Angle-Side)
   • D.SSS (Side-Side-Side)
   Answer: AAA (Angle-Angle-Angle)

   Explanation: AAA similarity criterion states that if all three angles of one triangle are equal to the corresponding angles of another triangle, the triangles are similar.

2. Q2Easy

   In the given figure, if a line is drawn parallel to BC intersecting AB and AC at D and E respectively, then which of the following is true?

   • A.AD/AB = AE/AC
   • B.AD/AB = DE/BC
   • C.AD/DB = AE/EC
   • D.AD/DB = AB/AC
   Answer: AD/AB = AE/AC

   Explanation: By the Basic Proportionality Theorem, if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally.

3. Q3Easy

   Which similarity criterion is used to prove that △ABC ~ △DEF if ∠A = ∠D, ∠B = ∠E, and ∠C = ∠F?

   • A.AAA (Angle-Angle-Angle)
   • B.SAS (Side-Angle-Side)
   • C.SSS (Side-Side-Side)
   • D.RHS (Right-Hypotenuse-Side)
   Answer: AAA (Angle-Angle-Angle)

   Explanation: AAA similarity criterion states that if all three angles of one triangle are equal to the corresponding angles of another triangle, the triangles are similar.

4. Q4Easy

   In the given figure, if a line parallel to BC intersects AB and AC at D and E respectively, then which of the following is true?

   • A.AD/DB = AE/EC
   • B.AD/DB = AB/AC
   • C.AD/DB = DE/BC
   • D.AD/AB = AE/AC
   Answer: AD/DB = AE/EC

   Explanation: By the Basic Proportionality Theorem, if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally.

5. Q5Easy

   Which similarity criterion is used to prove that △ABC ~ △DEF if AB/DE = BC/EF = AC/DF?

   • A.SSS (Side-Side-Side)
   • B.SAS (Side-Angle-Side)
   • C.AAA (Angle-Angle-Angle)
   • D.RHS (Right-Hypotenuse-Side)
   Answer: SSS (Side-Side-Side)

   Explanation: The SSS similarity criterion states that if the corresponding sides of two triangles are proportional, then the triangles are similar.

6. Q6Medium

   In the given figure, if △ABE ~ △CDE by AA similarity criterion, which of the following ratios is equal to BE/DE?

   • A.AB/CD
   • B.AE/CE
   • C.BE/CE
   • D.AB/BE
   Answer: AB/CD

   Explanation: Since △ABE ~ △CDE by AA similarity, the corresponding sides are proportional. Therefore, BE/DE = AB/CD.

7. Q7Medium

   In the figure, if DE is parallel to BC, then which of the following is true?

   • A.AD/DB = AE/EC
   • B.AD/DB = AB/AC
   • C.AD/DB = BC/AC
   • D.AE/EC = AB/BC
   Answer: AD/DB = AE/EC

   Explanation: By the Basic Proportionality Theorem (BPT), if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally.

8. Q8Medium

   If △ABC ~ △DEF, then which of the following ratios is equal to AB/DE?

   • A.BC/EF
   • B.AC/EF
   • C.AB/DE
   • D.BC/AC
   Answer: BC/EF

   Explanation: Since △ABC is similar to △DEF, their corresponding sides are proportional. Therefore, AB/DE = BC/EF.

9. Q9Medium

   If a line divides two sides of a triangle in the ratio 2:3, then the line is parallel to the third side. Which similarity criterion is being applied here?

   • A.AAA Similarity
   • B.Basic Proportionality Theorem (BPT)
   • C.SSS Similarity
   • D.RHS Similarity
   Answer: Basic Proportionality Theorem (BPT)

   Explanation: The Basic Proportionality Theorem states that if a line divides two sides of a triangle proportionally, then it is parallel to the third side.

10. Q10Hard

    In the given figure, if △ABD ~ △ACE, which of the following ratios is equal to BD/CE?

    • A.AB/AC
    • B.AD/CE
    • C.BD/AD
    • D.AC/AB
    Answer: AB/AC

    Explanation: Since △ABD ~ △ACE by similarity, the corresponding sides are proportional. Therefore, BD/CE = AB/AC.

11. Q11Hard

    If △ABC ~ △DEF, and AB = 5 cm, BC = 7 cm, AC = 6 cm, DE = 10 cm, then which of the following is the length of EF?

    • A.14 cm
    • B.12 cm
    • C.10 cm
    • D.11 cm
    Answer: 14 cm

    Explanation: Since △ABC ~ △DEF, the ratio of corresponding sides is equal. Therefore, BC/EF = AB/DE. Substituting the values, 7/EF = 5/10, which gives EF = 14 cm.

12. Q12Hard

    In the given figure, if △ABE ~ △CDE, then which of the following is true about the sides BE and DE?

    • A.BE/DE = AB/CD
    • B.BE/DE = AB/CE
    • C.BE/AB = DE/CD
    • D.BE/CD = AB/DE
    Answer: BE/DE = AB/CD

    Explanation: Since △ABE ~ △CDE, the corresponding sides are proportional. Therefore, BE/DE = AB/CD.

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