In triangle $$ABC$$ , $$\angle A = (3x + 10)°$$ , $$\angle B = (2x + 20)°$$ , and $$\angle C = (x + 30)°$$ . A student claims that triangle $$ABC$$ is an equilateral triangle. Is the student correct? Justify your reasoning.

Yes, because all angles simplify to $$60°$$ when $$x = 20$$ .

No, because the angles are $$70°$$ , $$60°$$ , and $$50°$$ when $$x = 20$$ .

Yes, because the sum of the angles equals $$180°$$ .

No, because the angles are $$80°$$ , $$60°$$ , and $$40°$$ when $$x = 20$$ .

A surveyor needs to determine whether a triangular plot of land with sides measuring $$50$$ m, $$120$$ m, and $$130$$ m is a right triangle. Using the Pythagorean theorem, which of the following correctly proves or disproves this?

$$50^2 + 120^2 = 130^2$$ is true, so it is a right triangle.

$$50^2 + 120^2 = 130^2$$ is false, so it is not a right triangle.

$$50^2 + 130^2 = 120^2$$ is true, so it is a right triangle.

$$120^2 + 130^2 = 50^2$$ is true, so it is a right triangle.

Two triangles share a common side. Triangle $$ABC$$ has sides $$AB = 7$$ , $$BC = 10$$ , and $$AC = 8$$ . Triangle $$ABD$$ has sides $$AB = 7$$ , $$BD = 12$$ , and $$AD = 8$$ . Using the Hinge Theorem, which angle is larger: $$\angle ACB$$ or $$\angle ADB$$ ?

$$\angle ADB$$ is larger because $$BD > BC$$ .

$$\angle ACB$$ is larger because $$BC

Both angles are equal because $$AB$$ and $$AD$$ are the same.

$$\angle ACB$$ is larger because $$AC = AD$$ .

In triangle $$DEF$$ , $$DE = 9$$ cm, $$EF = 12$$ cm, and $$\angle E = 90°$$ . A student wants to find the length of the altitude from $$E$$ to hypotenuse $$DF$$ . Which of the following correctly applies the geometric mean relationship to find the altitude $$h$$ ?

$$h = \frac{DE \times EF}{DF} = \frac{9 \times 12}{15} = 7.2$$ cm

$$h = \frac{DE + EF}{DF} = \frac{9 + 12}{15} = 1.4$$ cm

$$h = \sqrt{DE \times EF} = \sqrt{108} \approx 10.4$$ cm

$$h = \frac{DE^2}{DF} = \frac{81}{15} = 5.4$$ cm

In triangle $$ABC$$ , $$\angle B = 90°$$ , $$AB = 6$$ , and $$BC = 8$$ . Point $$D$$ is the midpoint of hypotenuse $$AC$$ . A student claims that $$BD = \frac{AC}{2}$$ . Which of the following best justifies or refutes this claim?

The claim is true because the median to the hypotenuse of a right triangle equals half the hypotenuse.

The claim is false because $$BD$$ must be calculated using the Pythagorean theorem directly.

The claim is false because $$BD$$ equals $$AC$$ in a right triangle.

The claim is true only if the triangle is isosceles.

In triangle $$ABC$$ , the perpendicular bisectors of the three sides meet at point $$O$$ . A student claims that $$O$$ is equidistant from all three vertices. Which theorem supports this claim, and what is the name of point $$O$$ ?

The Perpendicular Bisector Theorem; $$O$$ is the circumcenter.

The Angle Bisector Theorem; $$O$$ is the incenter.

The Centroid Theorem; $$O$$ is the centroid.

The Midsegment Theorem; $$O$$ is the orthocenter.

In triangle $$ABC$$ , $$AB = 13$$ , $$BC = 5$$ , and $$AC = 12$$ . A student wants to prove that triangle $$ABC$$ is a right triangle and then find the area. Which of the following correctly proves it is a right triangle and calculates the area?

$$5^2 + 12^2 = 13^2$$ , so it is a right triangle; Area $$= \frac{1}{2}(5)(12) = 30$$ sq units.

$$5^2 + 13^2 = 12^2$$ , so it is a right triangle; Area $$= \frac{1}{2}(5)(13) = 32.5$$ sq units.

$$12^2 + 13^2 = 5^2$$ , so it is a right triangle; Area $$= \frac{1}{2}(12)(13) = 78$$ sq units.

$$5^2 + 12^2 = 13^2$$ , so it is a right triangle; Area $$= \frac{1}{2}(5)(13) = 32.5$$ sq units.

Triangle Theorems and Relationships Quiz

Authored by Shanesha Anderson

Mathematics

10th Grade

B covered

Used 1+ times

Triangle Theorems and Relationships Quiz

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

B.E.S.T.MA.912.GR.1.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following correctly states the Triangle Inequality Theorem?

The sum of any two sides of a triangle must equal the third side.

The sum of any two sides of a triangle must be greater than the third side.

The difference of any two sides of a triangle must be greater than the third side.

The product of any two sides of a triangle must be greater than the third side.

Tags

B.E.S.T.MA.912.GR.1.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

B.E.S.T.MA.912.GR.1.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which theorem states that if two sides of a triangle are congruent, then the angles opposite those sides are congruent?

Triangle Inequality Theorem

Exterior Angle Theorem

Isosceles Triangle Theorem

Hinge Theorem

Tags

B.E.S.T.MA.912.GR.1.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Acute triangle

Obtuse triangle

Right triangle

Equilateral triangle

Tags

B.E.S.T.MA.912.GR.1.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

B.E.S.T.MA.912.GR.1.3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

B.E.S.T.MA.912.GR.1.3

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Triangle Theorems and Relationships Quiz

Which of the following correctly states the Triangle Inequality Theorem?

Which theorem states that if two sides of a triangle are congruent, then the angles opposite those sides are congruent?

Which of the following sets of side lengths can form a valid triangle?

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