Download notes 4-1 classifying triangles

NOTES 4-1 CLASSIFYING TRIANGLES KEY
Date _________________
CLASSIFYING TRIANGLES BY ANGLES
An acute triangle
An obtuse triangle
A right triangle
An equiangular triangle
In an acute triangle, all
In an obtuse triangle
In a right triangle one
In an equiangular
the angles are acute
one angle is obtuse.
angle is right.
triangle, all angles are
60°
Scalene Triangle
CLASSIFYING TRIANGLES BY THEIR SIDES
Isosceles Triangle
Equilateral Triangle
At least two sides are
congruent.
NO two sides are congruent
All three sides are congruent
In an isosceles triangle the two congruent sides are called legs. The angle formed by the legs is the
vertex angle. The other two angles are base angles. The side opposite the vertex is the base.
Triangle ABC is isosceles
A
What is the vertex? ∠A
What sides are legs? AB and AC
B
C
What side is the base? BC
What angles are base angles? ∠B and ∠C
1
1. Graph ∆ABC using points A(0, -4), B(0, -9) and C(-2, -5).
2. Classify ∆ABC.
a. Determine if ∆ABC is scalene, isosceles, or
equilateral. Explain your reasoning.
Scalene
b. Determine if ∆ABC is a right triangle. Explain
your reasoning. If it is not a right triangle, use
a protractor to determine what type of triangle
it is.
1
, and the slope on BC is −2 so the two line segments are
2
perpendicular, so the triangle is a right triangle., it is an obtuse triangle.
Yes, the slope on AC is
CLASSIFY QUADRILATERALS
DEFINITIONS
Quadrilateral: A polygon with four sides.
Parallelogram: A quadrilateral with both pairs of opposite sides parallel and congruent. Both
pairs of opposite angles are congruent. Consecutive angles are supplementary.
Diagonals bisect each other.
Rectangle: A parallelogram with four right angles. The diagonals are congruent.
Rhombus:
A parallelogram with four congruent sides. The diagonals are perpendicular. No
consecutive angles are congruent.
Square: A parallelogram with four congruent sides and four right angles. The diagonals are
perpendicular and congruent.
Trapezoid: A quadrilateral with exactly one pair of parallel sides called bases. The nonparallel
sides are called legs.
2
It is given that ABCD is a parallelogram. Graph
ABCD on the grids provided. Decide whether it is
a rectangle, rhombus, square or none of the above. Justify your answer using the definitions of the
quadrilaterals. Fill in the answers in the space provided and turn in this sheet.
1. Points: A(3, 1), B(3, -3), C(-2, -3), D(-2, 1)
SHAPE: Rectangle
Justification:
Opposite sides are congruent and perpendicular.
Therefore, we have 4 right angles, so we have
a parallelogram with 4 right angles and opposite
sides congruent.
D•
•A
C•
•B
2. Points: A(0, 4), B(6, -2), C(0, -2), D(-6, 4)
SHAPE: Parallelogram
Four sided polygon with no sides parallel.
D•
•A
C•
•B
3
3. Points: A(1, 1), B(3, 5), C(5. 1), D(3, -3)
SHAPE: RHOMBUS
Parallelogram with 4 congruent sides and
no consecutive angles congruent.
•B
•C
A•
•
D
4. Points: A(2, 5), B(5, 2), C(2, -1), D(-1, 2)
SHAPE: SQUARE
Justification: Parallelogram with 4
congruent sides and 4 right angles (slopes
are opposite reciprocals, therefore the
sides are perpendicular).
A•
•B
D•
•
C
4