Triangles

Match the types of triangles.

• Equilateral

• 
• Isosceles

• 
• Obtuse

• 
• Scalene

• 
• Right

• 

Select ALL that are TRUE statements about POLYGONS.

• A closed plane figure.

• Can be a circle.

• The number of vertices is the same as the number of sides.

• Named after the number of SIDES.

• Named after the number of VERTICES.

Answer explanation

Polygons are closed plane figures with sides and vertices. The number of vertices equals the number of sides, and they are named based on these sides or vertices. A circle is not a polygon.

Match the following:

• octagon

• 
• hexagon

• 
• decagon

• 
• hendecagon

• 
• heptagon

• 

This is a convex polygon.

• True

• False

Answer explanation

The statement is false because a convex polygon has all interior angles less than 180 degrees. If the polygon in question has any interior angle of 180 degrees or more, it is not convex.

This is a convex polygon.

• True

• False

Answer explanation

A convex polygon is defined as a polygon where all interior angles are less than 180 degrees and all vertices point outward. Since the statement confirms it is a convex polygon, the correct answer is True.

What is the value of x degrees?

Answer explanation

The value of x degrees is 0 because it is the only option that satisfies the condition given in the question. 64 is not correct.

Find the value of the unknown. (__ degrees)

Answer explanation

The unknown value is 0 degrees because it is the only option that satisfies the condition given in the question. The other choice, 50 degrees, does not fit the criteria.

The interior angles of an equilateral triangle always measures _______.

• a right angle

• 60 degrees

• to anything less than 180 degrees

• any number of degrees

Answer explanation

In an equilateral triangle, all three interior angles are equal. Since the sum of the angles in any triangle is 180 degrees, each angle measures 180/3 = 60 degrees. Therefore, the correct answer is 60 degrees.

Choose ALL that apply: What type of angle is BCD?

• exterior
• interior

• reflex

• acute

Answer explanation

Angle BCD is an exterior angle because it is formed outside the triangle by extending one of its sides. Exterior angles are created when a side of a polygon is extended, making BCD an exterior angle.

Any exterior angle is equal to...

• the sum of all three angles

• 180 degrees

• 90 degrees

• the sum of the opposite interior angles

Answer explanation

An exterior angle of a triangle is equal to the sum of the two opposite interior angles. This relationship is fundamental in geometry, making 'the sum of the opposite interior angles' the correct choice.