Geometric Figures, Terms, Vocabulary Review

Geometry - Basics of Geometry, Angles, Angle Relationships

BUILDING BLOCKS OF GEOMETRY

• POINT - an object in geometry that has zero dimension, and is represented by a dot

• LINE - an object that has one dimension, and extends infinitely

• PLANE - an object that has two dimensions, and extends infinitely

Line or Line Segment?

Continues forever (arrows) or ends!

Line Segment

A part of a line with a beginning and an end.

Plane

A flat, two-dimensional surface that extends infinitely far.

Ray

Collection of points with a beginning point but no end - continues forever in one direction.

Vertex

The point where two rays, lines, or line segments meet.

Vertex

A corner of a shape. Where two or more lines or line segments intersect.

Intersecting Lines

When two lines cross - like an intersection of two roads.

Types of Intersections

Learn them!

Parallel Lines

Two lines that never meet.

Perpendicular Lines

Meeting at 90 degrees.

Perimeter

The distance around a two-dimensional object or shape.

Area

The space a two dimensional object occupies, described in square units.

Angle

Two rays that meet at a certain vertex.

Notice that this angle can be identified four different ways!

ANGLES

• The intersection of two lines at a point (called a vertex)

• Measured in a unit called degrees

• When measuring, you use a tool called a protractor

Types of Angles

Learn them!

Interior Angles (Ángulos interiores)

Exterior Angles (Ángulos exteriores)

Opposite and congruent angles formed by the intersection of two lines.

​​Vertical Angles

Angles that have the same vertex, share a common side and do not overlap.

​​Adjacent Angles

Two angles are complementary if the sum of their measure is 90°

Complementary Angles

Two angles are supplementary if the sum of their measure is 180°

Supplementary Angles

Complementary Angles

Two or more angles that have a sum (add up to) of 90 degrees.

Supplementary Angles

Two or more angles with a sum of 180 degrees.

Notice how the relationship is written in symbols.

Vocabulary
Word Wall

supplementary angles: two angles that sum to 180o

30o + 150o= 180o→∠FGJ and ∠JGH are supplementary angles!

vertical angles: opposite, angles made by 2 intersecting lines

30o= 30o→∠JGF and ∠HGI are vertical angles! They are equal in size...

transversal

(or transversal line)

A transversal for a pair of
parallel lines is…
a line that meets each
of the parallel lines at
exactly one point

Line k is a transversal for
parallel lines l and m.

​

​The angles on the left are pairs that are equal. Los ángulos de la izquierda son los pares qu son iguales entre sí.

​The angles on the right are pairs that add up to 180^o. Los ángulos de la derecha son los pares que suman 180^o.

​1.

​2.

3.

​4.

Multiple Choice

Angles that have the same vertex, share a common side, and do not overlap.

• congruent angles

• complementary angles

• adjacent angles

• vertical angles

Multiple Choice

Angles whose sum of their measures that equals 90°

• congruent angles

• complementary angles

• adjacent angles

• supplementary angles

Multiple Choice

Opposite angles formed by the intersection of two lines. These angles are always congruent

• vertical angles

• complementary angles

• adjacent angles

• supplementary angles

Multiple Choice

Angles whose sum of their measures equals 180°

• congruent angles

• complementary angles

• adjacent angles

• supplementary angles

Fill in the Blanks

The common point where two rays meet

Multiple Choice

Which one of these represents a right angle?

Multiple Select

Name a pair of vertical angles... SELECT ALL THAT APPLY...

• b and c

• b and d

• c and a

• e and g

• $$60\degree$$  and f

Multiple Choice

A ___________ is an exact location. It has no size, no dimensions, only position.

• Point

• Line

• Segment

• Ray

• Parallel Lines

Multiple Choice

A ____________________ is straight (no bends), has no thickness, and extends in both directions without end (infinitely).

• Perpendicular Lines

• Parallel Lines

• Line

• Segment

• Ray

Multiple Choice

The point connecting lines, segments, or rays is called the ____________.

• vertex

• edge

• angle

Multiple Choice

An _______ is formed between two rays with the same endpoint and is measured in degrees.

• vertex

• angle

• edge

Multiple Choice

An angle is ___________ when its measure is 180° exactly.

• acute

• obtuse

• right

• straight

• reflex

Fill in the Blanks

If two figures have the same size and shape, then they are

Multiple Select

Select ALL the statements that are TRUE for the image above.

• $$c\parallel b,\ b\parallel a,\ c\parallel a$$  

• $$\overline{UT}\cong\overline{SR}$$  

• $$\overline{SR}\perp b,\ \overline{SR}\perp a$$  

• $$\overline{UT}\ and\ \overline{SR}$$  are transversal lines

• $$\overline{UT}\perp c,\ \overline{UT}\perp b$$  

Multiple Select

Select ALL the statements that are TRUE for the image above.

• $$\overline{CD}\ \perp CB$$

• $$\angle BCD\ \cong\ \angle BDC$$

• $$\angle C\ \cong\angle D$$

• $$BD\ \parallel\ CB$$

• $$CB\ and\ BD$$ forms $$\Delta CBD$$

Multiple Select

Select ALL the statements that are TRUE for the image above.

• $$\cdot S$$ is the midpoint in $$\overline{UR}$$

• $$\overline{UV}\ \parallel\ \overline{QR}$$

• $$\overrightarrow{UV}\ \parallel\ \overrightarrow{QR}$$

• $$\overline{US}\ \cong\ \overline{SR}$$

• $$\overline{ST}\ \perp\ \overline{UR}$$

Multiple Select

Select ALL the statements that are TRUE for the image above.

• $$\overleftarrow{X}\overrightarrow{V}\ \parallel\ \overleftarrow{U}\overrightarrow{T}$$

• $$\overline{US}\ \cong\ \overline{ST}$$

• $$\angle UST\ \cong\ \angle UTS$$

• $$\angle XWV\ \cong\ \angle UST$$

• $$\angle XWV\ =90\degree$$

Multiple Choice

TRUE OR FALSE:

Through any two points, there is exactly one line.

• True

• False

Multiple Select

Check off the two kinds of lines that can happen at the same time.

• Parallel

• Perpendicular

• Intersecting

• Skew

Multiple Choice

What kind of angle is this?

• Acute

• Obtuse

• Right

• Straight

Multiple Choice

What kind of angle is this?

• Acute

• Obtuse

• Right

• Straight

Multiple Choice

What kind of angle is this?

• Acute

• Obtuse

• Right

• Straight

Special Pairs of Angles

• Adjacent: " next to "

• Complementary " sum of 90° "

• Supplementary " sum of 180° "

• Vertical Angles "Across//always equal"

Multiple Select

What kind (or kinds) of angles are these:

• Adjacent

• Complementary

• Supplementary

• Vertical

Multiple Select

What kind (or kinds) of angles are these:

• Adjacent

• Complementary

• Supplementary

• Vertical

Multiple Select

What kind (or kinds) of angles are these:

• Adjacent

• Complementary

• Supplementary

• Vertical

Multiple Select

What kind (or kinds) of angles are these:

• Adjacent

• Complementary

• Supplementary

• Vertical

Multiple Select

What kind (or kinds) of angles are these:

• Adjacent

• Complementary

• Supplementary

• Vertical

Multiple Choice

What type of line does the picture represent?

• Parallel

• Intersecting

• Perpendicular

Multiple Choice

What type of line does the picture represent?

• Parallel

• Intersecting

• Perpendicular

Multiple Choice

What does this image show?

• parallel lines

• perpendicular lines

• intersecting lines

• line segments

Multiple Choice

What type of line does the picture represent? 

• Parallel

• Intersecting

• Perpendicular

Multiple Choice

What is this?

• Line segment

• Ray

• Point

• Line Segment

Multiple Choice

What is the term for a part of a line with two endpoints?

• point

• ray

• angle

• line segment

Multiple Choice

What is a name for this line?

Multiple Choice

What is this figure?

• Line

• Line with a point and arrow

• Ray

• Line segment