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Geometry
Label each figure with the information given.
1.
2.
PR = 7
= 105°
RO = 4
3.
AE = CD
4.
RU = US
VU = TU
RV = ST
Use the markings on the drawings to find the missing information.
5.
6.
_?_
_?_
7.
WX = _?_
ZY = _?_
= _?_
_?_
_?_
AE = _?_
In the diagram,
is a right angle. Name the figures
described.
8.
Two congruent
9.
supplementary angles
Two noncongruent
supplementary angles
10.
Two acute vertical
angles
11.
Two obtuse vertical angles
Draw and carefully label the figure described.
||
and
^
12.
Trapezoid ABCD with
.
13.
Scalene ∆MNP with MP = 3, PN = 5, and MN = 7.
14.
Hexagon RSTUVW with diagonal
15.
Isosceles right ∆XYZ with
16.
Trapezoid JKLM with
and
the non-parallel sides.
midpoint of
and Q be the midpoint of
. Draw PQ.
parallel to sides
and
.
.
Let P be the
Use your ruler and protractor to analyze the quadrilaterals below to discover
additional attributes (beyond the definition) about each.
Here is a parallelogram.
• What do you know about its sides?
• What do you know about its interior angles?
• Draw the two diagonals. What do you know about them?
Here is a rhombus.
• What do you know about its sides?
• What do you know about its interior angles?
• Draw the two diagonals. What do you know about them?
Here is a rectangle.
• What do you know about its sides?
• What do you know about its interior angles?
• Draw the two diagonals. What do you know about them?
Here is a square.
• What do you know about its sides?
• What do you know about its interior angles?
• Draw the two diagonals. What do you know about them?
Here is a trapezoid.
• What do you know about its sides?
• What do you know about its interior angles?
• Draw the two diagonals. What do you know about them?
Here is an isosceles trapezoid.
• What do you know about its sides?
• What do you know about its interior angles?
• Draw the two diagonals. What do you know about them?
Here is a kite.
• What do you know about its sides?
• What do you know about its interior angles?
• Draw the two diagonals. What do you know about them?
Additional Practice 3 (for use after Investigation 9)
Calculate each lettered angle measure and explain your reasoning for each
response.
a.
b.
c.
Geometry Unit Vocabulary
space: the set of all points.
collinear points: points that lie on the same line.
coplanar points: points that lie on the same plane.
line segment: that part of a line between and including two points.
ray: part of a line containing a point and all the points on the line to one side of
the
given point.
angle: two rays that share a common endpoint.
congruent segments: segments that have equal lengths.
congruent angles: angles that have equal measures.
right angle: angle whose measures is 90°
acute angle: angle whose measure is less than 90°
obtuse angle: angle whose measure is greater than 90°
angle bisector: ray that divides an angle into two equal parts
midpoint: point that divides line segment into two equal parts
parallel lines: coplanar lines that do not intersect
perpendicular lines: lines that meet at right (90°) angles
complementary angles: 2 angles whose sum is 90°
supplementary angles: 2 angles whose sum is 180°
vertical angles: 2 non-adjacent angles formed by intersecting lines
corresponding angles: angles on the same side of the transversal and same
side of
the coplanar lines
alternate interior angles: angles on either side of the transversal and in
between the
coplanar lines
polygon: closed figure formed by line segments
congruent polygons: polygons that have the same size and shape
diagonal: line segment joining 2 non-adjacent vertices of a polygon
equilateral polygon: polygon with all sides equal
equiangular polygon: polygon with all angles equal
regular polygon: equilateral, equiangular polygon
right triangle: triangle with one 90° angle
acute triangle: triangle with all angles acute
obtuse triangle: triangle with one obtuse angle
scalene triangle: triangle with no sides equal
isosceles triangle: triangle with two sides equal
equilateral triangle: triangle with all sides equal
trapezoid: quadrilateral with one pair of parallel sides
parallelogram: quadrilateral with two pairs of parallel sides
rhombus: equilateral parallelogram (or quadrilateral)
rectangle: equiangular parallelogram (or quadrilateral)
square: (1) regular quadrilateral, or
(2) equiangular rhombus, or
(3) equilateral rectangle
kite: quadrilateral with two pairs of adjacent congruent sides
Other vocabulary that can be introduced:
coplanar lines: lines that lie on the same plane
skew lines: non-coplanar lines that do not intersect
linear pair: 2 adjacent angles that form a line
vertex angle: angle between the two equal sides of an isosceles triangle
base angles: angles opposite the two equal sides of an isosceles triangle
median: line segment joining vertex with midpoint of opposite side in a triangle
midsegment: line segment joining two midpoints in a polygon
altitude: line segment from vertex perpendicular to opposite side in a triangle
height: (1) length of an altitude in a triangle
(2) length of perpendicular segment connecting parallel sides in a
quadrilateral
segment bisector: line that passes through midpoint of a segment
perpendicular bisector of a segment: line that divides segment into two equal
parts and is perpendicular to the segment