Triangles and Triangles and QuadrilateralsQuadrilateralsSpecial names and properties for Special names and properties for these polygonsthese polygons

Naming Triangles:Naming Triangles:

Triangles are named by observing their Triangles are named by observing their angles as well as their sides.angles as well as their sides.

We have special names that correspond We have special names that correspond to their angles, and there are names that to their angles, and there are names that correspond to their sides.correspond to their sides.

Naming Triangles Naming Triangles

If a triangle has just one angle which If a triangle has just one angle which measures 90measures 90°, then the triangle is called °, then the triangle is called a RIGHT triangle.a RIGHT triangle.

Right Triangles

NOT Right Triangles

Is it possible to have a Is it possible to have a triangle which has two 90° triangle which has two 90° angles?angles?

NOW what ??

Conclusion: There exists no triangles with two 90° angles.

Acute TriangleAcute Triangle

If all 3 angles of a triangle measure less than If all 3 angles of a triangle measure less than 9090°, then the triangle is an acute triangle.°, then the triangle is an acute triangle.

Acute Triangles

NOT acute triangles

Obtuse TriangleObtuse Triangle

If just one angle of a triangle is greater If just one angle of a triangle is greater than 90than 90°, then the triangle is obtuse.°, then the triangle is obtuse.

Obtuse Triangles

NOT obtuse triangles

Naming Triangles based Naming Triangles based on their side lengths:on their side lengths:

A triangle is SCALENE, if none of the A triangle is SCALENE, if none of the three sides are congruent.three sides are congruent.

Scalene Triangles

NOT scalene triangles

Equilateral TrianglesEquilateral Triangles

If all 3 sides of a triangle are congruent, If all 3 sides of a triangle are congruent, then the triangle is equilateral.then the triangle is equilateral.

Isosceles TrianglesIsosceles Triangles

If two sides of a triangle are congruent, If two sides of a triangle are congruent, then it is an isosceles triangle.then it is an isosceles triangle.

NOT isosceles triangles

Isosceles Triangles

Name these triangles as Name these triangles as specific as possible:specific as possible:

QUADRILATERALSQUADRILATERALS

Every quadrilateral will fit into one of 6 Every quadrilateral will fit into one of 6 categories.categories. Trapezoid, Kite, Parallelogram, Rhombus, Trapezoid, Kite, Parallelogram, Rhombus,

Rectangle, and Square.Rectangle, and Square. They depend upon how many sets of lines They depend upon how many sets of lines

are parallel (0, 1, or 2), how many pairs of are parallel (0, 1, or 2), how many pairs of sides are congruent, and how many angles sides are congruent, and how many angles are congruent.are congruent.

QUADRILATERAL QUADRILATERAL FLOWCHARTFLOWCHART

QUADRILATERALS

How many sets of parallel sides does the quadrilateral have??

If 0 is the answer, then the quadrilateral is a ‘KITE’.

If 1 is the answer, then the quadrilateral is a ‘TRAPEZOID’

If there are 2 sets of parallel lines, then the figure is some type of PARALLELOGRAM!

(IF the two non-parallel sides are congruent, it is an isosceles trapezoid)

‘RHOMBUS’

Both sets of lines are parallel, and all sides are congruent!

RECTANGLE

SQUAREAll 4 sides equal, all 4 90° angles

If 0 is the answer, then the quadrilateral is a ‘KITE’.

TRAPEZOIDTRAPEZOID

If a quadrilateral has just one pair of If a quadrilateral has just one pair of parallel lines, then it is a trapezoidparallel lines, then it is a trapezoid

PARALLELOGRAMPARALLELOGRAM

A quadrilateral is a parallelogram if it has A quadrilateral is a parallelogram if it has TWO sets of parallel linesTWO sets of parallel lines

RHOMBUSRHOMBUS

A quadrilateral is a RHOMBUS, if it has A quadrilateral is a RHOMBUS, if it has two sets of parallel lines AND all 4 sides two sets of parallel lines AND all 4 sides are congruent.are congruent.

RECTANGLERECTANGLE

A Quadrilateral is a Rectangle if it has A Quadrilateral is a Rectangle if it has two sets of parallel lines, and all 4 angles two sets of parallel lines, and all 4 angles are congruent (RIGHT angles).are congruent (RIGHT angles).

SQUARESQUARE

A quadrilateral is a square if it has two A quadrilateral is a square if it has two sets of parallel lines, 4 congruent sides, sets of parallel lines, 4 congruent sides, and 4 congruent angles (RIGHT angles).and 4 congruent angles (RIGHT angles).

KITEKITE

This quadrilateral has no sets of parallel This quadrilateral has no sets of parallel lines.lines.

CLASSWORK/HOMEWORKCLASSWORK/HOMEWORK

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