Download Section 12.1: Geometric Shapes

Section 12.1:
Geometric Shapes
• line segment: set of all points created when joining two points in the shortest possible
way.
• angle: is the union of 2 line segments with a common endpoint, called a vertex.
• triangle: closed figures composed of exactly three line segments.
* The three line segments are called sides.
* Triangles have three angles.
• Triangles described by sides:
* scalene triangle: A triangle that has three sides that are different lengths.
* isosceles triangle: A triangle with two or three sides the same length.
* equilateral triangle: A triangle with all three sides the same length.
• Triangles described by angles:
* right triangle: A triangle which has a right angle. (Right angle: is an angle
formed by perpendicular lines; it measures 90◦ .)
* equiangular triangle: A triangle with all three angles equal.
IMPORTANT: The sum of the measures of the angles of a triangle
is 180◦ .
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SECTION 12.1: GEOMETRIC SHAPES
• quadrilaterals: closed figures composed of four line segments.
• Types of quadrilaterals:
* square: quadrilateral with 4 sides the same length AND 4 right angles.
* rectangle: quadrilateral with 4 right angles.
* kite: quadrilateral with two nonoverlapping pairs of adjacent sides that are the
same length.
* rhombus: quadrilateral with 4 sides the same length.
* trapezoid: quadrilateral with EXACTLY one pair of parallel sides.
* parallelogram: quadrilateral with 2 pairs of parallel sides.
IMPORTANT: The sum of the measures of the angles of a
quadrilateral is 360◦ .
SECTION 12.1: GEOMETRIC SHAPES
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Example 1: Draw a diagram for each of the following or tell why it is not possible.
(a) A rhombus that is not a square.
(b) A rhombus with four acute angles.
(c) A rectangle that is not a square.
(d) A parallelogram that is not a rectangle or a rhombus.
(e) A trapezoid with no lines the same length.
• Congruent line segments: are line segments which have the same length.
• Congruent angles: are angles which are exact copies of each other; have the same
measurement. Note that orientation does not matter.
• equilateral: any figure whose sides are congruent.
• equiangular: any figure whose angles are congruent.
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SECTION 12.1: GEOMETRIC SHAPES
Example 2: Several shapes are pictured here. Sides with the same length are indicated, as
are right angles.
c
b
a
f
e
d
g
i
h
k
(a) Which figures have a right angle?
(b) Which figures have at least one pair of parallel sides?
(c) Which figures have at least two sides with the same length?
(d) Which figures have all sides the same length?
(e) Identify all triangles as scalene, isosceles, or equilateral.
(f) Identify all rhombuses.
(g) Identify all trapezoids.
(h) Identify all kites.
SECTION 12.1: GEOMETRIC SHAPES
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Example 3: Find the following shapes in the figure.
B
A
C
K
J
I
Q R
L
M
O
D
N
P
H
G
(a) Three squares.
(b) A rectangle that is not a square.
(c) A parallelogram that is not a rectangle.
(d) A rhombus that is not a square.
(e) A kite that is not a rhombus.
(f) A scalene triangle with no right angle.
(g) A right scalene triangle.
(h) A trapezoid that is not isosceles.
(i) An isosceles trapezoid.
F
E