true or false
True or False: A triangle can have angles that measure 0°, 90°, and 90°.
False (Sum would be 180°, but 0° is not a valid angle in a triangle)
1. Which of the following could NOT be the angles of a triangle?
A) 60°, 60°, 60°
B) 90°, 45°, 45°
C) 120°, 30°, 30°
D) 100°, 50°, 40°
Answer: ✅ C (120° + 30° + 30° = 180°, but a triangle can only have one angle over 90°)
True or false:A triangle can have more than one obtuse angle.
❌ False
→ Only one angle in a triangle can be greater than 90°, or the sum will exceed 180°.
What is the measure of each angle in an equilateral triangle?
A) 45°
B) 60°
C) 90°
D) 120°
✅ Answer: B
The incircle of a triangle is tangent to all three sides, and its center is the point of concurrency of the angle bisectors.
✅ True
True or False: You can create a triangle where the sides are all irrational numbers but the angles are all rational numbers.
True (For example, equilateral triangle with side √2 — all angles are 60°)
6. What is the measure of an exterior angle of a triangle if the two opposite interior angles are 40° and 65°?
A) 35°
B) 75°
C) 105°
D) 115°
Answer: ✅ C (Exterior = sum of remote interior angles = 40° + 65° = 105°)
true or false :If a triangle is both isosceles and right, its angles must be 45°, 45°, and 90°.
✅ True
The centroid of a triangle is the point where:
A) The angle bisectors meet
B) The altitudes meet
C) The medians meet
D) The perpendicular bisectors meet
✅ Answer: C
Which triangle center is the only one that is guaranteed to lie inside every triangle?
A) Circumcenter
B) Incenter
C) Orthocenter
D) Centroid
Answer: B
→ The incenter is always inside; others can be outside in obtuse triangles
In triangle geometry, it is possible for all medians, altitudes, and angle bisectors to be the same line.
True (Only in an equilateral triangle)
8. Which point in a triangle is always inside the triangle, regardless of the type?
A) Circumcenter
B) Orthocenter
C) Centroid
D) All of the above
✅ C (The centroid is always inside)
The medians of a triangle always intersect at a point outside the triangle.
❌ False
→ The centroid (median intersection) is always inside
1. In triangle ABC, angle A = 2x, angle B = 3x, and angle C = x + 30°. What is the measure of angle A?
A) 40°
B) 50°
C) 60°
D) 70°
✅ Answer: B
→ 2x + 3x + (x + 30) = 180 → 6x + 30 = 180 → x = 25 → angle A = 2×25 = 50°
If the lengths of the sides of a triangle are in the ratio 1:1:2, it must be an isosceles triangle.
❌ False
→ A triangle with sides 1, 1, and 2 does not satisfy the triangle inequality → not possible.
The measure of an exterior angle of a triangle is equal to the sum of the two adjacent interior angles.
False (It equals the sum of the two remote interior angles)
10. Which triangle has no line of symmetry?
A) Equilateral triangle
B) Isosceles triangle
C) Scalene triangle
D) Right isosceles triangle
Answer: ✅ C
true or false: A triangle with sides 3 cm, 4 cm, and 8 cm is valid.
❌ False
→ 3 + 4 = 7, which is less than 8 → Not valid.
. What is the missing angle in a triangle with angles 50° and 70°?
A) 50°
B) 60°
C) 40°
D) 30°
✅ Answer: C (180 – 120 = 60°)
In an equilateral triangle, the centroid, orthocenter, circumcenter, and incenter all coincide at the same point. Which of the following is not true for this triangle?
A) The centroid is the center of mass.
B) The orthocenter is the intersection of the altitudes.
C) The circumcenter is equidistant from all vertices.
D) The incenter is equidistant from all sides.
✅ Answer: D
The incenter is indeed equidistant from all sides, but in equilateral triangles, all centers coincide at one point.
True or False: If the incenter, circumcenter, and centroid of a triangle are the same point, the triangle must be equilateral.
True (This only happens in equilateral triangles)
3. Which of the following is always true about the exterior angles of a triangle?
A) Each is larger than any interior angle
B) Their sum is 180°
C) Their sum is 360°
D) There are always 2 exterior angles
Answer: ✅ C
true or false If two angles of one triangle are equal to two angles of another triangle, the triangles must be similar.
✅ True
→ Two equal angles imply the third is also equal → AAA similarity
. Which of these is not always true about all triangles?
A) The sum of all interior angles is 180°
B) The longest side is opposite the largest angle
C) Every triangle has at least one 90° angle
D) The exterior angles add up to 360°
✅ Answer: C
12. Multiple Choice:
For an isosceles triangle with side lengths a=8a = 8a=8, b=8b = 8b=8, and c=6c = 6c=6, what is the measure of the angle between the two equal sides?
A) 45°
B) 60°
C) 90°
D) 120°
✅ Answer: C
→ Use the law of cosines or the area formula, and you’ll get the angle between the two equal sides is 90°.