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CHAPTER 7
7-1 LINES AND PLANES
• Point – a location, has no size, name point by capital letter
• Line – series of points that extend in opposite directions
without end
• Ray – part of a line with one endpoint and all the points of
the line on one side of the endpoint
• Segment – part of a line with two endpoints and all points
in between.
7-1 LINES AND PLANES
• Plane – Flat surface that extends indefinitely in all
directions and has no thickness
• Intersecting Lines – have exactly one point in common
• Parallel Lines – lines in the same plane that never
intersect
• Skew Lines – lie in different planes, they are neither
parallel or intersecting
7-1 LINES AND PLANES
7-1 LINES AND PLANES
Name segments that fit
description.
1) parallel to BC
2) intersect BH
3) skew to AG
7-1 LINES AND PLANES-ANSWERS
Name segments that fit
description.
1) parallel to BC- HD
2) intersect BH – AB, BC
3) skew to AG – BC, HD
7-2 IDENTIFYING AND CLASSIFYING ANGLES
Angle – figure formed by two rays
with a common endpoint
Vertex – point of intersection of two
sides of an angle or figure
7-2 IDENTIFYING AND CLASSIFYING ANGLES
Classify angles by their measures:
7-2 IDENTIFYING AND CLASSIFYING ANGLES
Complementary angles – sum of the measures of two
angles is 90°
Supplementary angles – sum of the measures of two
angles is 180°
1) Find complement of m<G = 79°
2) Find supplement of m<G = 12°
3) Find complement of m<G = 75.1°
4) Find supplement of m<G = 82.2°
7-2 IDENTIFYING AND CLASSIFYING ANGLESANS
Complementary angles – sum of the measures of two
angles is 90°
Supplementary angles – sum of the measures of two
angles is 180° 1) Find complement of m<G = 79° 11°
2) Find supplement of m<G = 12° 168°
3) Find complement of m<G = 75.1°
14.9°
4) Find supplement of m<G = 82.2° 97.8°
7-2 IDENTIFYING AND CLASSIFYING ANGLES
Adjacent angles – share a vertex and a side. They are
side by side.
Vertical angles – formed by two intersecting lines and
are opposite each other
Congruent – same size and shape
7-2 IDENTIFYING AND CLASSIFYING ANGLES
7-2 IDENTIFYING AND CLASSIFYING ANGLESANS
Right angle
Obtuse angle
Straight angle
Acute angle
Acute angle
Right angle
7-2 IDENTIFYING AND CLASSIFYING ANGLES
1) Four right angles
2) Two pairs of obtuse
vertical angles
1) two lines
2) Three segments
3) Pair of congruent angles
3) Two pairs of adjacent
supplementary
angles
7-2 IDENTIFYING AND CLASSIFYING ANGLESANS
1) two lines XU, ST, XP
2) Three segments XN, XP,
QN
3) Pair of congruent angles
<VXW and <UXP
1) Four right angLes
<QNT, <SNQ, <SNY,
<YNT
2) Two pairs of obtuse
vertical angles
<MSW AND <UST ;
<SXP AND <VXW
3) Two pairs of adjacent
supplementary
angles <MSX AND
<MSU; <MSX AND
<XST
7-3 TRIANGLES
Classifying Triangles by Sides:
7-3 TRIANGLES
Classifying Triangles by angle measures:
7-3 TRIANGLES
Classifying Triangles by angle measures:
7-3 TRIANGLES -ANS
Classifying Triangles by angle measures:
Obtuse scalene
right isosceles
acute isosceles
7-3 TRIANGLES
Classifying Triangles by angle measures:
7-3 TRIANGLES-ANS
Classifying Triangles by angle measures:
isoseles
right
equilateral
right
obutse
acute
7-3 TRIANGLES
Angle Sum of a Triangle:
- Sum of the measures of the angles of any
triangle is 180°
- All angles add up to 180° inside a triangle.
7-3 TRIANGLES-ANS
Angle Sum of a Triangle:
- Sum of the measures of the angles of any
triangle is 180°
- All angles add up to 180° inside a triangle.
40°
80°
64°
7-4 QUADRILATERALS AND OTHER POLYGONS
Regular polygon – a polygon with all sides
congruent and all angles congruent
Irregular polygon – a polygon with sides that are
not all congruent or angles that are not all
congruent
7-4 QUADRILATERALS AND OTHER POLYGONS
Trapezoid – one pair of parallel sides
Parallelogram – both pairs of opposite sides parallel
Rectangle – 4 right angles
Rhombus – 4 congruent sides
Square – 4 right angle angles and 4 congruent sides
7-4 QUADRILATERALS AND OTHER POLYGONS
7-4 QUADRILATERALS AND OTHER POLYGONSANS
hexagon, regular
pentagon, irregular
Pentagon, regular
parallelogram,
irregular
quadrilateral, irregular
7-5 CONGRUENT FIGURES
Congruent Polygons – are polygons with the
same size and same shape.
Name corresponding parts.
7-5 CONGRUENT FIGURES-ANSWERS
Congruent Polygons – are polygons with the
same size and same shape.
Name corresponding parts.
7-5 CONGRUENT FIGURES
7-5 CONGRUENT FIGURES-ANSWERS
QR
<R
YW
<X
7-5 CONGRUENT FIGURES
7-5 CONGRUENT FIGURES-ANSWERS
Not congruent, because
corresponding angles
and sides are not
congruent.
Congruent, because
corresponding angles
and sides are
congruent.
7-6 CIRCLES
Circle – set of points in a plane that are all the same distance
from a given point.
Radius – segment that connects the center of a circle to circle.
Chord – segment that has both endpoints on the circle.
Diameter – chord that passes through the center of the circle;
longest chord
Central Angle – angle with a vertex at the center of the circle
Arc – part of a circle
Semicircle – is half a circle
7-6 CIRCLES
Identify radius, chord, diameter, central angle,
and arc.
7-6 CIRCLES
7-6 CIRCLES-ANSWERS
FG, EF
<FDG, <GDH
FH
Triangle FDG
Arcs, FG, FGH, GH, HE, GHE
90°
FH
7-7 CIRCLE GRAPHS
Circle graph – graph of data in which a circle represents
the whole. Total must be = to 100%
Finding central angles:
7-7 CIRCLE GRAPHS
7-7 CIRCLE GRAPHS-ANSWERS
75 °
60 °
120 °
48
20.8%
16.7%
33.3%
105 °
29.2%
360°
100%
7-7 CIRCLE GRAPHS
7-7 CIRCLE GRAPHS-ANSWERS
sleeping
12.5%
About 8 hours