1.5 Triangles and Special Quadrilaterals
Triangles:
_____________________ – A triangle with one right angle. The side opposite the right
angle is the hypotenuse. The other two sides are the legs.
hypotenuse
leg
leg
______________________ – A triangle with three acute angles.
67
62
51
______________________ – A triangle with one obtuse angle.
26
36
118
_______________________ – A triangle with three sides of different lengths.
2.5
4.3
5.0
______________________________ – A triangle with three congruent sides.
_______________________________ – A triangle with three congruent angles.
Geometry Lesson 1.5: Triangles and Special Quadrilaterals
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______________________________ – A triangle with at least two congruent sides. If the
triangle has exactly two congruent sides, they are called legs and the angle between them is
called the vertex angle. The side opposite the vertex angle is called the base. The nonvertex
angles are called base angles.
vertex 
leg
leg
base 
base
base 
Quadrilaterals:
______________________ – A quadrilateral with exactly one pair of parallel sides. The
parallel sides are called bases. A pair of angles that have a base as a common side are called
a pair of base angles.
base 's
base
base
base 's
________ – A quadrilateral with exactly two pairs of distinct congruent consecutive sides.
The angles between the pairs of congruent sides are called the vertex angles. The angles
between the pairs of noncongruent sides are called the nonvertex angles.
nonvertex angles
vertex angles
__________________ – A quadrilateral in which both pairs of opposite sides are parallel.
Any of the sides, or its length, can be designated as a base. An altitude is a line segment
Geometry Lesson 1.5: Triangles and Special Quadrilaterals
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from the base, ending at and perpendicular to a line containing the opposite side. The height
is the length of an altitude.
____________ – An equilateral parallelogram
______________ – An equiangular parallelogram.
________________ – An equiangular rhombus or an equilateral rectangle. A regular
quadrilateral.
Geometry Lesson 1.5: Triangles and Special Quadrilaterals
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Things You Can Assume:
lines are straight
if two lines intersect, they intersect at one point
points on a line are collinear
points in a diagram are coplanar unless distinct planes are drawn to show that
they are noncoplanar
Things You Can Not Assume:
lines are parallel (unless they are marked as parallel)
lines are perpendicular (unless they are marked as perpendicular)
angles are congruent (unless they are marked as congruent)
segments are congruent (unless they are marked as congruent)
polygons are congruent (unless they are marked as congruent)
Example 1: Identify which lines are perpendicular, which lines are parallel, and which pairs
of triangles are congruent.
A
B
C
E
G
D
F
H
I
J
K
L
N
M
A
U
V
W
C
B
D
Geometry Lesson 1.5: Triangles and Special Quadrilaterals
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Example 2: a) Locate a point C so that ABC is an isosceles triangle.
b) Locate point D so that ABD is a right triangle.
6
4
2
B
A
-5
5
-2
-4
Homework: pp. 64 – 65 => 1 – 16
Geometry Lesson 1.5: Triangles and Special Quadrilaterals
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