Chapter 3, Problem 1RP

a

To determine

To distinguish the statement “Two triangles are congruent if two sides and an angle of one are congruent to the corresponding parts of the other” in either of A, S or N

Answer to Problem 1RP

Final answer for the statement is S

Explanation of Solution

Given information:

The following statement has been given

Two triangles are congruent if two sides and an angle of one are congruent to the corresponding parts of the other

We know that the property states that two triangles can be congruent only if the two sides are congruent and the angle containing them is also congruent.

Thus, this statement is not always true

b

To determine

To distinguish the statement “If two sides of a right triangle are congruent to the corresponding parts of the other right triangle, the triangles are congruent” in either of A, S or N

Answer to Problem 1RP

Final answer for the statement is A

Explanation of Solution

Given information:

The following statement has been given

If two sides of a right triangle are congruent to the corresponding parts of the other right triangle, the triangles are congruent

We know that using Pythagoras theorem, the other side of the triangle will also be congruent, thus we can say that the statement given is always true

c

To determine

To distinguish the statement “All three altitudes of a triangle fall outside the triangle” in either of A, S or N

Answer to Problem 1RP

Final answer for the statement is N

Explanation of Solution

Given information:

The following statement has been given

All three altitudes of a triangle fall outside the triangle

We know that only for an obtuse angled triangle, one altitude fall outside the triangle.

Thus the given statement is never true

d

To determine

To distinguish the statement “A median of a triangle does not contain the midpoint of the side to which it is drawn” in either of A, S or N

Answer to Problem 1RP

Final answer for the statement is N

Explanation of Solution

Given information:

The following statement has been given

A median of a triangle does not contain the midpoint of the side to which it is drawn

We know that a median of a triangle ends at the midpoint of the side to which it is drawn

Thus, the given statement is never true

e

To determine

To distinguish the statement “A right triangle is congruent to an obtuse triangle” in either of A, S or N

Answer to Problem 1RP

Final answer for the statement is N

Explanation of Solution

Given information:

The following statement has been given

A right triangle is congruent to an obtuse triangle

We know that a right triangle can never have an obtuse angle. Thus, the given statement is never true