Which of the following statements is false?1. All equilateral triangle

1.	Which of the following statements is false?1. All equilateral triangles are similar2. All 30° – 60° – 90° triangles are similar3. All 45° – 45° – 90° triangles are similar4. All isosceles triangles are similar
Answer» Correct Answer - Option 4 : All isosceles triangles are similar Concept: Following are the properties of similarities of triangle: 1) AAA - When all angle of both the triangle are equal then they are similar. 2) SAS - When two sides and angle between them of two triangle are equal then they are similar. 3) SSS - When all the sides of both the triangle are in same proportion then they are similar. Calculation: Now, We will go through the options. By option (1), In all the equilateral triangle all the sides in same proportion. So they are similar by AAA property. By option (2) and (3), If both the triangle has equal angle like 30° – 60° – 90° or 45° – 45° – 90° they are similar by AAA property. By option (4), In all isosceles triangles two side are proportional but third side can't be always proportional neither angle between them are always equal. ∴ Two isosceles triangle can not always be similar.

Which of the following statements is false?1. All equilateral triangles are similar2. All 30° – 60° – 90° triangles are similar3. All 45° – 45° – 90° triangles are similar4. All isosceles triangles are similar

Answer» Correct Answer - Option 4 : All isosceles triangles are similar

Concept:

Following are the properties of similarities of triangle:

1) AAA - When all angle of both the triangle are equal then they are similar.

2) SAS - When two sides and angle between them of two triangle are equal then they are similar.

3) SSS - When all the sides of both the triangle are in same proportion then they are similar.

Calculation:

Now, We will go through the options.

By option (1),

In all the equilateral triangle all the sides in same proportion.

So they are similar by AAA property.

By option (2) and (3),

If both the triangle has equal angle like 30° – 60° – 90° or 45° – 45° – 90° they are similar by AAA property.

By option (4),

In all isosceles triangles two side are proportional but third side can't be always proportional neither angle between them are always equal.

∴ Two isosceles triangle can not always be similar.