In triangles ABC and PQR, AB = AC, &ang;C =&ang;P and &ang;B =&ang;Q. The two triangles are:

Neither congruent nor isosceles

Triangles Test: Can You Pass This Trivia Quiz?

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| By Tanmay Shankar

Tanmay Shankar

Community Contributor

Quizzes Created: 491 | Total Attempts: 1,797,843

Questions: 15 | Attempts: 471 | Updated: Mar 19, 2023

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Questions and Answers

1.
- A.
- B.
- C.
- D.
Correct Answer
B.
2.

D is a point on the side BC of a ΔABC such that AD bisects ∠BAC. Then
- A.
  
  BD = CD
- B.
  
  CD > CA
- C.
  
  BD > BA
- D.
  
  BA > BD
Correct Answer
D. BA > BD

Explanation
In triangle ABC, D is a point on side BC such that AD bisects angle BAC. Since AD is the angle bisector, it divides angle BAC into two equal angles. By the Angle Bisector Theorem, BD/DC = BA/AC. Since AC is positive and BD is positive, we can conclude that BA must be greater than BD for the equation to hold true. Therefore, the correct answer is BA > BD.

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3.

It is given that Δ ABC ≅ Δ FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true?
- A.
  
  DF = 5 cm, ∠F = 60°
- B.
  
  DF = 5 cm, ∠E = 60°
- C.
  
  DE = 5 cm, ∠E = 60°
- D.
  
  DE = 5 cm, ∠D = 40°
Correct Answer
B. DF = 5 cm, ∠E = 60°

Explanation
Since ΔABC ≅ ΔFDE, corresponding sides and angles of the two triangles are equal. Given that AB = 5 cm, it implies that DF = 5 cm. Also, since ∠A = 80°, it implies that ∠E = 80° (corresponding angles). However, none of the given options matches this condition. Therefore, the correct answer cannot be determined based on the given information.

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4.

All the medians of a triangle are equal in case of a:
- A.
  
  Scalene triangle
- B.
  
  Right angled triangle
- C.
  
  Equilateral triangle
- D.
  
  Isosceles triangle
Correct Answer
C. Equilateral triangle

Explanation
In an equilateral triangle, all three sides are equal in length. Since the medians of a triangle connect each vertex to the midpoint of the opposite side, they will also be equal in length in an equilateral triangle. This is because the medians split each side into two equal parts, resulting in three congruent segments. Therefore, all the medians of an equilateral triangle are equal.

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5.

In triangle PQR if ∠Q = 90^o, then:
- A.
  
  PQ is the longest side
- B.
  
  QR is the longest side
- C.
  
  PR is the longest side
- D.
  
  None of these
Correct Answer
C. PR is the longest side

Explanation
In a right triangle, the longest side is always the hypotenuse, which is the side opposite the right angle. In triangle PQR, if angle Q is 90 degrees, then PR is the hypotenuse and therefore the longest side.

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6.

In the given figure, PS is the median then ∠QPS?
- A.
  
  40^o
- B.
  
  50^o
- C.
  
  80^o
- D.
  
  90^o
Correct Answer
B. 50^o

Explanation
Since PS is the median, it divides the triangle into two congruent parts. Therefore, angles QPS and QSP must be equal. Since the sum of the angles in a triangle is 180 degrees, angle QPS must be 180 - (90 + 40) = 50 degrees.

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7.

In the given figure, if the exterior angle is 135^o then ∠P is:
- A.
  
  45^o
- B.
  
  60^o
- C.
  
  80^o
- D.
  
  90^o
Correct Answer
D. 90^o

Explanation
In the given figure, the exterior angle is formed by extending one side of the triangle. The exterior angle and the interior angle (angle P) are supplementary angles, meaning they add up to 180 degrees. Since the exterior angle is given as 135 degrees, angle P can be calculated by subtracting 135 degrees from 180 degrees. Therefore, angle P is 45 degrees.

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8.

In the given figure, AB = AC and ∠B = 50^o then; ∠A is:
- A.
  
  50^o
- B.
  
  80^o
- C.
  
  100^o
- D.
  
  130^o
Correct Answer
B. 80^o

Explanation
In the given figure, AB = AC and ∠B = 50o. Since AB = AC, this implies that triangle ABC is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are also equal. Therefore, ∠A = ∠C. Since ∠B = 50o, and the sum of the angles in a triangle is 180o, we can deduce that ∠A + ∠B + ∠C = 180o. Substituting the given values, we have ∠A + 50o + ∠A = 180o. Simplifying this equation, we get 2∠A = 130o. Dividing both sides by 2, we find that ∠A = 65o. Therefore, the correct answer is 80o.

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9.

In a triangle ABC, ∠B = 35^o and ∠C = 60^o, then
- A.
  
  ∠A = 80^o
- B.
  
  ∠A = 85^o
- C.
  
  ∠A = 120^o
- D.
  
  ∠A = 145^o
Correct Answer
B. ∠A = 85^o

Explanation
In a triangle, the sum of the angles is always 180 degrees. Therefore, to find the measure of angle A, we can subtract the measures of angles B and C from 180 degrees. Angle B is given as 35 degrees and angle C is given as 60 degrees. Subtracting these from 180 gives us 85 degrees, which is the measure of angle A.

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10.

If in ΔPQR, PQ = PR then:
- A.
  
  ∠P=∠R
- B.
  
  ∠P=∠Q
- C.
  
  ∠Q=∠R
- D.
  
  None of these
Correct Answer
A. ∠P=∠R

Explanation
If in triangle PQR, PQ = PR, it means that the lengths of the two sides PQ and PR are equal. In an isosceles triangle, the angles opposite to these equal sides are also equal. Therefore, if PQ = PR, it implies that angle P is equal to angle R.

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11.

In triangles ABC and PQR, AB = AC, ∠C =∠P and ∠B =∠Q. The two triangles are:
- A.
  
  Isosceles but not congruent
- B.
  
  Isosceles and congruent
- C.
  
  Congruent but not isosceles
- D.
  
  Neither congruent nor isosceles
Correct Answer
A. Isosceles but not congruent

Explanation
The given information states that in triangles ABC and PQR, AB = AC, ∠C = ∠P, and ∠B = ∠Q. This means that triangle ABC has two sides (AB and AC) that are equal in length, making it an isosceles triangle. However, the triangles are not congruent because there is no information given about the lengths of the other sides or the measures of the other angles. Therefore, the correct answer is "Isosceles but not congruent."

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12.

In triangles ABC and DEF, AB = FD and ∠A =∠D. The two triangles will be congruent by SAS axiom if:
- A.
  
  BC = EF
- B.
  
  AC = DE
- C.
  
  AC = EF
- D.
  
  BC = DE
Correct Answer
B. AC = DE

Explanation
In order for the triangles to be congruent by SAS (Side-Angle-Side) axiom, the corresponding sides and the included angle of the triangles must be equal. Given that AB = FD and ∠A = ∠D, the only remaining condition that needs to be satisfied is AC = DE. Therefore, the correct answer is AC = DE.

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13.

If DE = QR, EF = PR and FD = PQ, then
- A.
- B.
- C.
- D.
Correct Answer
B.
14.
- A.
  
  80^o
- B.
  
  40^o
- C.
  
  50^o
- D.
  
  100^o
Correct Answer
C. 50^o
15.

Two sides of a triangle are of length 5 cm and 1.5 cm. The length of the third side of the triangle cannot be:
- A.
  
  3.6 cm
- B.
  
  4.1 cm
- C.
  
  3.8 cm
- D.
  
  3.4 cm
Correct Answer
D. 3.4 cm

Explanation
The length of the third side of a triangle must be less than the sum of the lengths of the other two sides and greater than the difference between the lengths of the other two sides. In this case, the sum of the lengths of the other two sides is 5 cm + 1.5 cm = 6.5 cm, and the difference between the lengths of the other two sides is 5 cm - 1.5 cm = 3.5 cm. Therefore, the length of the third side cannot be 3.4 cm, as it is less than the difference between the lengths of the other two sides.

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