Chapter 8, Problem 20RP

a

To determine

To find: The following statement lies in which section i.e. A, S and N.

Answer to Problem 20RP

Always true,thetwo isosceles triangles are congruent, if base angles are congruent

Explanation of Solution

Given information:

Base angles are congruent

Since base angles are congruent

And, isosceles triangles have two sides equal

Then corresponding sides will be also congruent

Hence, isosceles triangles will be always congruent

b

To determine

To Check: The given statement is always, sometimes or never be true.

Answer to Problem 20RP

Sometimes true, the two isosceles triangles will be similar, if vertex angles are congruent

Explanation of Solution

Given information:

The following statement is given

“Two isosceles triangles are similar, if one of the vertex angle of the one is congruent to the vertex angle of the other.”

Vertex angles are congruent

Then angles containing two sides of triangles will be not always equal

Hence, sometimes it is true that isosceles triangles are similar

c

To determine

To find:The following statement” An equilateral triangle is similar to scalene triangle” is always, sometimes or never be true.

Answer to Problem 20RP

Never true, the equilateral triangle is similar to scalene triangle

Explanation of Solution

Given information:

The equilateral triangle is similar to scalene triangle

The equilateral triangle has all sides and angles equal,

The scalene triangle has all sides and angles unequal

Therefore, no condition of similarity satisfies

Hence, statement is never true

d

To determine

To check: The statement “If two sides of one triangle are proportional to two sides of another triangle, the triangles are similar” is always, sometimes or never be true.

Answer to Problem 20RP

The statement is Always true.

Explanation of Solution

Given information:

Corresponding sides are in proportion in two triangles

Since, corresponding sides are in proportion, it follows that tringles will always be similar, as per basic proportionate theorem

e

To determine

To check: The $\Delta ABC$ is congruent to $\Delta RST$ for the given condition lies in which of the section i.e. A,S or N.

Answer to Problem 20RP

Always true, two triangles will be similar

Explanation of Solution

Given information:

One angle and two sides of two triangles are in proportion

Always true, Using Basic ProportionateTheorem, triangles will be similar if ratio of their corresponding sides are in proportion

f

To determine

To check: The following statement “The line intersecting a triangle at trisection and is parallel to second side then it will pass through the trisection of third side” is always, sometimes or never be true.

Answer to Problem 20RP

Always true, it will follow, basic proportionate theorem

Explanation of Solution

Given information:

Line intersects one side of triangle at its trisection and parallel to second side

Always true, because the sides of triangle follow Basic Proportionate theorem

g

To determine

The statement “The two right angles are similar if their legs are in proportion” is always, sometimes or never be true.

Answer to Problem 20RP

Always true, the right angles will be similar

Explanation of Solution

Given information:

Legs are in proportion of two right angle triangles

According to basic proportionate theorem, right angle triangles will be similar

h

To determine

The given statement “The ratio of perimeters of two polygons will be in the ratio 5: 6 if their two sides are in ration 3:4” lies in which section i.e. A, S or N.

Answer to Problem 20RP

Never true, the ratio of perimeters will be in the ratio 5:6

Explanation of Solution

Given information:

Two sides in a polygon are in ratio of 3:4

Polygon will always have more than two sides and perimeter is sum of the sides of polygon.

Thus, it is never true that perimeter will be in the ration 5:6