Chapter 3 - Must Know Geometry

An acute angle, is an angle that measures between _______________

0° and 90°

The sum of the angles of a triangle always equals:

180°

An obtuse angle is an angle measuring between _________________

90° and 180°

median

A segment drawn from a vertex of the triangle to the midpoint of the opposite side

Acute Triangle

A triangle that contains 3 angles that are less than 90°.

obtuse triangle

A triangle that contains one angle greater than 90° (obtuse angle).

Right Triangle

A triangle that has a 90 degree angle.

equilateral triangle

A triangle with three congruent sides (equal in length)

Altitude is not: A) a perpendicular bisector B) a straight line C) possible from all vertexes of a triangle

A) a perpendicular bisector

The median, altitude, and angle bisector of an isosceles triangle are all the same segment when: A) coming from the vertex angle of the isosceles triangle B) the isosceles is obtuse and the segment is drawn through the smallest angle C) the isosceles is pretty

A) coming from the vertex angle of the isosceles triangle

an altitude can be a perpendicular bisector if: A) drawn from the from the vertex angle of an isosceles triangle B) drawn in scalene triangle C) drawn in right triangle

A) drawn from the from the vertex angle of an isosceles triangle

To find the possible lengths of the third side of a triangle, you need to know that the third side has to be ________________ than the ___________________ of the two given sides, but ___________________ than the ____________________ of the two given sides. A) larger than the difference / but smaller than the sum B) smaller that the sum / but larger than the sum of the three angles

A) larger than the difference / but smaller than the sum

The largest side of a triangle is always found: A) opposite of the largest angle B) opposite of the top angle C) opposite of the smallest angle

A) opposite of the largest angle

When you label your triangles - read the question carefully - the letter that should be at the top, the vertex, should be the letter _____________ A) that appears in both congruent sides (example AB & BC - therefore B) B) that appears at the first position in the triangle (🔺ABC - so A) C) that is the last one (🔺ABC - so C)

A) that appears in both congruent sides (example AB & BC)

If two sides of a triangle are equal, then _______________ A) the angles opposite to them are equal B) the third angle is obtuse C) it is a scalene triangle

A) the angles opposite to them are equal

Midpoints and segment bisectors divide a segment into ____________________ A) two congruent segments B) two right angles C) ugly segments

A) two congruent segments

In a triangle, an angle bisector can be drawn from any of the three angles. A) yes B) no C) maybe

A) yes

When sides of a triangle are equal - the _________________ A) triangles are beautiful B) angles opposite of them are equal C) the base angles are congruent

B) angles opposite of them are equal

When using side length we can classify triangles as: A) right, small, and medium B) isosceles, equilateral, and scalene C) scalene, right, and obtuse

B) isosceles, equilateral, and scalene

The smallest side of a triangle is always found: A) opposite of the largest side B) opposite of the smallest side C) on the other side of the triangle

B) opposite of the smallest side

When an Altitude meets the opposite side of the triangle it forms a: A) beautiful angle B) right angle C) obtuse angle

B) right angle

Triangles can be classified by ______________ and ________________. A) angle measurement and size of one side B) side lengths and angle measurement C) angle direction and sides direction

B) side lengths and angle measurement

The angle formed from the two equal sides in a isosceles is called: A) point B) vertex angle C) top angle B) base angle

B) vertex angle

If the median, altitude, and angle bisector are all the same segment when drawn from the vertex angle of an isosceles triangle, then the median, altitude and angle bisector are all the same segment when drawn from any of the three angles of _________________ A) equilateral triangle B) equiangular triangle C) A & B

C) A & B

Since equilateral triangles have 3 equal angles, what can we deduct about the measurement of the angles in an equilateral triangles? A) they are all obtuse B) there is at least one right angle C) all angles are acute 60°

C) all angles are acute 60°

An isosceles triangle has 2 equal angles called __________ A) basic angles B) pointy angles C) base angles

C) base angles

The Exterior Angle of a triangle is formed when we: A) draw a quadrilateral next to it B) bisect the larges angle C) extend a side of a triangle through a vertex of the triangle

C) extend a side of a triangle through a vertex of the triangle

What kind of triangle can be classified using both its angle measure and it's side length? A) right triangle B) beautiful triangle C) isosceles

C) isosceles

When using angle measurement we can classify triangles as: A) right, not right, and pointy B) isosceles, right, and small C) right, obtuse, and acute

C) right, obtuse, and acute

What is referred to as the vertex angle in an isosceles triangle? A) the angle that is the smallest in the right triangle B) the angle with the largest measure in an isosceles C) the angle created between the equal sides in isosceles

C) the angle created between the equal sides in isosceles

If the angles of a a triangle are all unequal, then ___________________ A) the triangle is ugly B) the triangle is wrong C) the lengths of its sides are also unequal

C) the lengths of its sides are also unequal

You can't always create a triangle out of three segments. What role has to be met to create a triangle? A) you need to have all segments equal B) the segments need to add up to 180 C) the sum of the two smallest sides has to be greater than the largest side of the triangle

C) the sum of the two smallest sides has to be greater than the largest side of the triangle

The exterior angle is adjacent to the: A) only to the largest angle B) only to the right angle C) to the corresponding angle inside of the triangle

C) to the corresponding angle inside of the triangle

A scalene triangle is ________ A) a weirdo B) a ugly triangle C) triangle with all sides unequal and all angles unequal

C) triangle with all sides unequal and all angles unequal

The median connects to the: A) midpoint B) center of the opposite side C) not sure D) A & B

D) A & B

What is another word we can use to describe equilateral triangles?

Equiangular

A right angle measures ___________

Exactly 90°

How can you find an exterior angle in a triangle?

It is the sum of the two nonadjacent interior angles

What allows us to solve for unknown sides and angles in a triangle algebraically?

Knowing the properties of the different kinds of triangles

What are median, altitude, and angle bisectors?

Special segments that can be drawn inside triangles that play a major role in the geometry of triangles.

What determines whether a triangle is acute, obtuse, isosceles equilateral, scalene, or right?

The angle measurements and side lengths of the triangle.

The Exterior Angle Theorem says __________

The exterior angle of a triangle is equal to the sum of the two nonadjacent angles of the triangle.

What is one of the most important properties of a triangle?

The sun of the three angles of s triangle must equal 180°

angle bisector

a ray that divides an angle into two congruent angles

altitude of a triangle

a segment that extends from any angle of a triangle and is perpendicular to the line containing the opposite side

What is an isosceles triangle?

a triangle that contains two equal sides

What are base angles in an isosceles triangle?

the angles that are opposite to the two equal sides

The largest side of a triangle is always found opposite the ________________

the largest angle of the triangle

A triangle is a polygon that contains_______________

three sides and three angles called vertices