1.
Which of the following triangles are always similar?

A.
Right triangle

B.
Obtuse triangle

C.
Equilateral triangle

D.
Isoceles triangle
Correct Answer
C. Equilateral triangleExplanation
Equilateral triangles are always similar because all three sides are equal in length and all three angles are equal. This means that if you have two equilateral triangles, you can scale one up or down and rotate it, and it will still be congruent to the other triangle. Therefore, all equilateral triangles are similar to each other.Rate this question:

2.
The sides of a triangle are 7,10, and 12. Find the length of the longest side of a similar triangle whose shortest side is 21.

A.
12

B.
21

C.
30

D.
36
Correct Answer
D. 36Explanation
In a similar triangle, the corresponding sides are proportional. To find the length of the longest side of the similar triangle, we can set up a proportion using the given lengths of the sides.Let x be the length of the longest side of the similar triangle.
Using the proportion:
7/21 = 12/x
Crossmultiplying:
7x = 21 * 12
Simplifying:
7x = 252
Dividing both sides by 7:
x = 36
Therefore, the length of the longest side of the similar triangle is 36.
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3.
In triangle ABC, angle A = 90º and angle B = 25º. In triangle DEF, angle E = 25º and angle F = 65º. Are the triangles similar?

A.
False

B.
True
Correct Answer
B. TrueExplanation
Yes, the triangles are similar. Since angle B in triangle ABC is equal to angle E in triangle DEF, and angle A in triangle ABC is equal to angle F in triangle DEF, by the AngleAngle (AA) similarity criterion, the triangles are similar.Rate this question:

4.
Two triangles are similar. If the ratio of the perimeters is 5:3, find the ratio of the corresponding sides.

A.
5:3

B.
15:9

C.
25:9

D.
1:8
Correct Answer
A. 5:3Explanation
If two triangles are similar, it means that their corresponding angles are equal, and the ratio of their corresponding sides is the same. In this case, the ratio of the perimeters of the triangles is given as 5:3. The perimeter of a triangle is the sum of its three sides. Since the ratio of the perimeters is 5:3, it means that the sum of the corresponding sides of the triangles is also in the ratio of 5:3. Therefore, the ratio of the corresponding sides of the triangles is 5:3.Rate this question:

5.
Find the unknown length x in the following figure.
Correct Answer
156.
Which of the following conditionsare NOT sufficient to identify a pair of congruent triangles?

A.
Three pairs of corresponding sides are proportional (SSS).

B.
Two pairs of corresponding sides are proportional and their included angles are equal (SAS).

C.
Two pairs of corresponding sides are proportional and one pair of nonincluded angles are equal (SSA).

D.
Two pairs of angles are equal (AA).
Correct Answer
C. Two pairs of corresponding sides are proportional and one pair of nonincluded angles are equal (SSA).Explanation
The condition that is NOT sufficient to identify a pair of congruent triangles is "Two pairs of corresponding sides are proportional and one pair of nonincluded angles are equal (SSA)." While the SideSideAngle (SSA) condition may suggest similarity, it alone is not enough to guarantee congruence between triangles.Rate this question:

7.
What is true of angles of similar triangles?

A.
Opposite angles are congruent.

B.
Corresponding angles are congurent.

C.
Corresponding angles are 90 degrees.

D.
Corresponding angles are parallel
Correct Answer
B. Corresponding angles are congurent.Explanation
In similar triangles, corresponding angles are congruent. This means that if two triangles are similar, the corresponding angles in each triangle have the same measure. This property is a key characteristic of similar triangles and is used to determine if two triangles are similar or not. Opposite angles being congruent, corresponding angles being 90 degrees, and corresponding angles being parallel are not true for all similar triangles.Rate this question:

8.
Area of an equilateral triangle with side length a is equal to:

A.
√3/5a

B.
√3/4a

C.
√3/4 a^{2}

D.
√2/3a
Correct Answer
C. √3/4 a^{2}Explanation
The correct answer, √3/4 a^2, represents the formula for finding the area of an equilateral triangle. In this formula, "a" represents the length of one side of the triangle. The square of "a" (a^2) is multiplied by the constant √3/4 to find the area. This formula is derived from the geometric properties of equilateral triangles and is a commonly used formula in mathematics.Rate this question:

9.
If the perimeter of a triangle is 100 cm and the length of the two sides are 30 cm and 40 cm, the length of the third side will be:

A.
30

B.
45

C.
24

D.
16
Correct Answer
A. 30Explanation
The perimeter of a triangle is the sum of the lengths of all its sides. In this case, the perimeter is given as 100 cm. The length of the two sides are given as 30 cm and 40 cm. To find the length of the third side, we subtract the sum of the lengths of the two given sides from the perimeter. So, 100  (30 + 40) = 30 cm. Therefore, the length of the third side is 30 cm.Rate this question:

10.
The height of an equilateral triangle of side 5 cm is:

A.
5 cm

B.
6.66 cm

C.
4.33 cm

D.
2.44 cm
Correct Answer
C. 4.33 cmExplanation
The height of an equilateral triangle can be found using the formula h = (√3/2) * s, where h is the height and s is the length of a side. Plugging in the given side length of 5 cm into the formula, we get h = (√3/2) * 5 = 4.33 cm. Therefore, the correct answer is 4.33 cm.Rate this question:

FAQs
How do you prove triangles similar answers? ›
AA (AngleAngle): If triangles have two of the same angles, then the triangles are similar. SAS (SideAngleSide): If triangles have two pairs of proportional sides and equal included angles, then the triangles are similar.
How do you know whether two triangles are similar it is enough to know? ›To prove triangles are similar, you need to prove two pairs of corresponding angles are congruent.
How do you test for similarity of triangles? ›If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar. Thus, if ∠A = ∠X and AB/XY = AC/XZ then ΔABC ~ΔXYZ.
What are the four rules for similar triangles? › AA. : Two pairs of corresponding angles are equal.
 SSS. : Three pairs of corresponding sides are proportional.
 SAS. : Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.
Determine whether the triangle with the missing side is smaller or larger. If the triangle is smaller, divide its corresponding side in the larger triangle by k to get the missing side. Otherwise, multiply the corresponding side in the smaller triangle by k to find the missing side.
What are the 3 theorems that prove triangles are similar? ›The Language of Similarity
These theorems, which are Angle  Angle (AA), Side  Angle  Side (SAS) and Side  Side  Side (SSS), make it possible to determine triangle similarity with minimal calculations.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.
What is the 45 45 90 triangle? ›454590 triangle means a triangle with two 45 degree angles and one 90 degree angle. A 454590 triangle has two sides that are of equal length, called the legs. The third side is longer than the other two and is called the hypotenuse and is always opposite the right angle.
What is an example of a similar triangle? ›Similar Triangles Examples
Similar triangles are triangles for which the corresponding angle pairs are equal. That means equiangular triangles are similar. Therefore, all equilateral triangles are examples of similar triangles.
If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. If ∠A ≅ ∠D and ∠B ≅ ∠E, then △ABC ∼ △DEF.
What is the test for similar triangles in geometry? ›
 Angle Angle Angle (AAA) If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar. ...
 Side Angle Side (SAS) ...
 Side Side Side (SSS) ...
 Rightangle Hypotenuse Side (RHS)
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.
What is the formula for similar right triangles? ›If the lengths of the corresponding legs of two right triangles are proportional, then by SideAngleSide Similarity the triangles are similar. In the figure, A B P Q = B C Q R . So, Δ A B C ∼ Δ P Q R .