7-8 6 th grade math Quadrilaterals

Objective To classify and draw quadrilaterals. Find missing angles in quadrilaterals. Why? To further your knowledge in measurement and geometry and keeping building a strong foundation in MG in HS

California State Standards MG 2.3: Draw quadrilaterals … from information about them (e.g., quadrilateral having equal sides but no right angles, …). AF 1.1 : Write and solve one-step linear equations with one variable. AF 3.2: Express in symbolic form simple relationships arising from geometry. MG 2.0: Identify and describe the properties of two-dimensional figures. MR 2.2: Apply strategies and results from simpler problems to more complex problems.

Vocabulary Quadrilateral – A polygon with 4 sides. Sum of all 4 angles = 360 ° Diagonal – A segment that joins two vertices (plural of vertex) of a polygon, but is not a side. A diagonal divides a quadrilateral into two triangles.

Vocabulary Trapezoid – A quadrilateral with only one pair of opposite sides parallel or Parallelogram – A quadrilateral with each pair of opposite sides parallel and congruent. A rectangle with no right angles. Rhombus – A parallelogram with all sides congruent. A square with no right angles.

Vocabulary Rectangle – A parallelogram with 4 right angles. 2 pairs of congruent sides. Square – A parallelogram with all sides congruent and 4 right angles.

How to Find Missing Angles in Quadrilaterals 1) Add the 3 known angles 2) Subtract 360 from Step 1 3) Check work Quadrilateral with 3 known angles: 90 ° + 90 ° ° 360 ° - (90 ° + 90 ° °) = 360 ° = 65 °

How to Find Missing Angles in Quadrilaterals Find the missing angle measures in quadrilateral JKLM. K L r u M s 150° J ┐ t ┌ 45° N To solve take apart slowly. Look for adjacent, vertical, complementary, supplementary angles A) m ∠ r = m ∠ r is supplementary to ∠ L (150°) m ∠ r = 180 – 150 = 30° B) m ∠ t = m ∠ t is ½ of ∠ N m ∠ t = 45° C) m ∠ u= m ∠ u is part of ∠ r and 45° 180 – ( ) m ∠ u= = 105° D) m ∠ s= m ∠ s is part of quadrilateral sJ150 ° t = 360 – (s ) m ∠ s = 75 °

Try It! Find the missing angle n and classify the polygon. 1) 2) 3) 4) 1)90 °, rectangle (all angles add to 360) 2)70 °, parallelogram (all angles add to 360 and vertical angles are equal) 3)110 °, trapezoid (all angles add to 360 and opposite angles are equal) 4)40°, quadrilateral (all angles add to 360)

Objective Review To classify and draw quadrilaterals. Find missing angles in quadrilaterals. Why? To You now have furthered your knowledge in measurement and geometry and keeping building a strong foundation in MG in HS Quadrilaterals are classified according to the special properties of their sides and angles. Knowing the properties for complementary and supplementary angles, and the sums of the angle measures of triangles and quadrilaterals can help you find the measure of an unknown angle.

Independent Practice Complete problems Copy original problem first. Show all work! If time, complete Mixed Review: If still more time, work on Accelerated Math.