Triangles and Quadrilaterals Special names and properties for these polygons

Naming Triangles: Triangles are named by observing their angles as well as their sides. We have special names that correspond to their angles, and there are names that correspond to their sides.

Naming Triangles If a triangle has just one angle which measures 90°, then the triangle is called a RIGHT triangle. NOT Right Triangles Right Triangles

Is it possible to have a triangle which has two 90° angles? NOW what ?? Conclusion: There exists no triangles with two 90° angles.

Acute Triangle If all 3 angles of a triangle measure less than 90°, then the triangle is an acute triangle. NOT acute triangles Acute Triangles

Obtuse Triangle If just one angle of a triangle is greater than 90°, then the triangle is obtuse. NOT obtuse triangles Obtuse Triangles

Naming Triangles based on their side lengths: A triangle is SCALENE, if none of the three sides are congruent. NOT scalene triangles Scalene Triangles

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

Isosceles Triangles If two sides of a triangle are congruent, then it is an isosceles triangle. Isosceles Triangles NOT isosceles triangles

Name these triangles as specific as possible:

QUADRILATERALS Every quadrilateral will fit into one of 6 categories. Trapezoid, Kite, Parallelogram, Rhombus, Rectangle, and Square. They depend upon how many sets of lines are parallel (0, 1, or 2), how many pairs of sides are congruent, and how many angles are congruent.

QUADRILATERAL FLOWCHART QUADRILATERALS How many sets of parallel sides does the quadrilateral have?? If there are 2 sets of parallel lines, then the figure is some type of PARALLELOGRAM! If 0 is the answer, then the quadrilateral is a ‘KITE’. If 0 is the answer, then the quadrilateral is a ‘KITE’. If 1 is the answer, then the quadrilateral is a ‘TRAPEZOID’ ‘RHOMBUS’ RECTANGLE Both sets of lines are parallel, and all sides are congruent! (IF the two non-parallel sides are congruent, it is an isosceles trapezoid) SQUARE All 4 sides equal, all 4 90° angles

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

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

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

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

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

KITE This quadrilateral has no sets of parallel lines.

CLASSWORK/HOMEWORK Page 64, #2-16 Page 65, 66, #25-29