Question

1. (l30) if a triangle is equilateral, then it is also

a. isosceles
b. obtuse
c. scalene
d. either a or b
e. none of the above

1. (l34) two right triangles are congruent if the hypotenuse and leg of one are

the corresponding parts of the other.
a. similar to
b. proportionate to
c. greater than
d. congruent to
e. none of the above

1. (l29) an acute triangle is

isosceles.
a. always
b. sometimes
c. never
d. definitely
e. none of the above

1. (l29) if a triangle is equilateral, then it is

a right triangle.
a. always
b. sometimes
c. never
d. definitely
e. none of the above

1. (l32) given (\triangle srocong\triangle tor) in the diagram below, (angle sorcong)

a. (angle rto)
b. (angle rmo)
c. (angle tmo)
d. (angle tro)
e. none of the above

Explanation:

1. For the first question:

• An equilateral triangle has all three sides equal. An isosceles triangle has at least two sides equal. So an equilateral triangle is a special case of an isosceles triangle.
• An equilateral triangle has each angle equal to \(60^{\circ}\), so it is not obtuse (an obtuse triangle has one angle greater than \(90^{\circ}\)). A scalene triangle has all sides of different lengths.

2. For the second question:

• The Hypotenuse - Leg (HL) congruence theorem states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent.

3. For the third question:

• An acute triangle (all angles less than \(90^{\circ}\)) can be isosceles (e.g., a triangle with angles \(70^{\circ},70^{\circ},40^{\circ}\)) or not isosceles (e.g., a triangle with angles \(60^{\circ},50^{\circ},70^{\circ}\)). So an acute triangle is sometimes isosceles.

4. For the fourth question:

• An equilateral triangle has each angle equal to \(60^{\circ}\). A right - triangle has one angle equal to \(90^{\circ}\). So an equilateral triangle can never be a right - triangle.

5. For the fifth question:

• Since \(\triangle SRO\cong\triangle TOR\), by the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) property, \(\angle SOR\cong\angle TRO\).

Answer:

1. A. isosceles
2. D. congruent to
3. B. sometimes
4. C. never
5. D. \(\angle TRO\)