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Name:________________________________________________________________________________Date:_____/_____/__________ Spiral Back: Evaluate the following when x = -2 and y = 3 1) -4y – x + (3+ x2) Let’s see what you remember! Solve the following equations: 2) x – 6 = -20 3) 2x – 2 = -16 4) 3 4 x = 10 5) When multiplying or dividing by a _________________ number, we SWITCH the inequality sign! Solve AND graph the following inequalities (SWITCH SIGN when needed): 6) x + 3 > -7 7) -5x ≥ 20 8) -4 < 𝑥 2 Today’s Lesson: What: Quadrilaterals Why: To introduce basic geometry vocabulary and focus on quadrilateral relationships. What do you remember?? Prior Knowledge/ Essential Vocabulary . . . same size and Congruent– objects that are the __________ shape. Line— goes ________________ in both directions. (⟷ ) forever one direction. ( ⟶ ) Ray— goes forever in _________ Line Segment– has both a beginning and an _______. end ( ─ ) Parallel Lines– two or more lines that will never intersect . ( | | ) ________________ Perpendicular – two line segments/ lines that meet right in such a way that ___________ angles are formed. (⏊) Prior Knowledge/ Essential Vocabulary . . . point where two line segments meet. Vertex — __________ lines come together Angle— formed when two _________ at the same vertex. 90° . less than ______ Acute Angle— measures ________ more than ______ 90° . Obtuse Angle–measures ________ 90° . Right Angle– measures exactly ______ Prior Knowledge/ Essential Vocabulary . . . 3 or Polygon— simple, closed figure formed by _____ segments . Polygons more line ________________ curved . are NOT __________ 3 sides. Triangle — _____ 4 sides. Quadrilateral — _____ Pentagon — _____ 5 sides. 6 sides. Hexagon— _____ 7 sides. Heptagon — _____ 8 sides. Octagon — _____ 9 sides. Nonagon — _____ Decagon — _____ 10 sides. Adjacent Sides— two sides of a polygon that share the same ___________ vertex (side-by-side). opposite Opposite Sides— sides that are directly ______________ from one another. Quadrilateral Vocabulary . . . Vocabulary: 4 angles. 4 sides and ________ Quadrilateral– closed figure with ______ Trapezoid– has one pair of ____________ parallel sides. parallel and opposite sides Parallelogram– opposite sides ___________ congruent ____________. The diagonals in every parallelogram _____________ bisect eachother (cuts shape into 2 equal parts). Rectangle– parallelogram with 4 __________ right angles. congruent sides. Square– parallelogram with 4 right angles and 4 ______________ Rhombus– parallelogram with 4 congruent ___________ sides . 360 degrees in every quadrilateral! There is a total of ___________ Quadrilaterals . . . How ARE they rELATED? ALWAYS UP, SOMETIMES DOWN, NEVER SIDE-to-SIDE! Quadrilateral SORTING LAB (teacher will give directions) Examples of “Congruency” and “Parallel” Notation: congruent parallel Quadrilateral characteristics . . . Only 1 set of parallel sides 2 sets of parallel sides Kite √ √ √ 4 congruent sides √ √ √ √ 2 sets of congruent sides √ √ Opposite angles congruent √ √ √ √ Diagonals bisect the figure √ √ √ √ MUST have 4 right angles Trapezoid Square Rhombus Rectangle Parallelogram Place a check mark in the appropriate boxes: √ √ √ END OF LESSON The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed. NOTE: The last slide(s) in any lesson slideshow represent the homework assigned for that day. NAME: Math-7 NOTES DATE: ______/_______/_______ What: Quadrilaterals Why: To introduce basic geometry vocabulary and focus on quadrilateral relationships. Prior Knowledge/ Essential Vocabulary Congruent– objects that are the __________ size and shape. Line— goes ________________ in both directions. (⟷ ) Ray— goes forever in _________ direction. ( ⟶ ) Line Segment– has both a beginning and an _______. ( ) Parallel Lines– two or more lines that will never ________________ . ( I I ) Perpendicular – two line segments/ lines that meet in such a way that ___________ angles are formed. (┴) Vertex — __________ where two line segments meet. Angle— formed when two _________ come together at the same vertex Acute Angle— measures ________ than ______ . Obtuse Angle–measures ________ than ______ . Right Angle– measures exactly ______ . Polygon— simple, closed figure formed by _____ or more line ________________ . Polygons are NOT __________ . Triangle — _____ sides. Quadrilateral — _____ sides. Pentagon — _____ sides. Hexagon— _____ sides. Heptagon — _____ sides. Octagon — _____ sides. Nonagon — _____ sides. Decagon — _____ sides. Adjacent Sides— two sides of a polygon that share the same ___________ (side-by-side). Opposite Sides— sides that are directly ________________ from one another. Quadrilateral Vocabulary: Quadrilateral– closed figure with ______ sides and ________ angles. Trapezoid– has one pair of ____________ sides. Parallelogram– opposite sides ___________ and opposite sides ____________. The diagonals in any parallelogram _________________ eachother (cuts shape into 2 equal parts). Rectangle– parallelogram with 4 __________ angles. Square– parallelogram with 4 right angles and 4 ______________ sides. Rhombus– parallelogram with 4 congruent ___________ . There is a total of ___________ degrees in every quadrilateral! HOW ARE quadrilaterals RELATED? ALWAYS UP, SOMETIMES DOWN, NEVER SIDE-to-SIDE! Examples of “Congruency” and “Parallel” Notation: 4 sides congruent Matching tick marks mean those sides are _________________. Top congruent to bottom/ Left congruent to right . . . Matching arrow marks mean those sides are _________________. Top parallel to bottom/ Left parallel to right . . . Quadrilateral characteristics . . . Place a check mark in the appropriate boxes: Parallelogram Only 1 set of parallel sides 2 sets of parallel sides 4 congruent sides 2 sets of congruent sides Opposite angles congruent Diagonals bisect the figure MUST have 4 right angles Rectangle Rhombus Square Trapezoid Kite Name:__________________________________________________________________________________ Date: _____/_____/__________ “Quadrilateral Characteristics” True or False (correct “False” answers in order to make them “True”): 1) _____ Every square is also a rhombus. 2) _____ Every rhombus is also a square. 3) _____ Every rectangle is a parallelogram. 4) _____ Parallelograms have opposite sides that are perpendicular. 5) _____ A square is a special type of trapezoid. 6) _____ Not all rectangles are squares. 7) _____ It is impossible for a square to also be a rectangle. 8) _____ A trapezoid is a parallelogram. 9) _____ Every trapezoid is also a quadrilateral. 10) _____ A quadrilateral can have more than four angles. 11) _____ The trapezoid is the only quadrilateral that is NOT a parallelogram. 12) _____ SpongeBob has square pants. Name:____________________________________________________________________________________Date:_____/_____/__________ “Analyzing Quadrilaterals” Circle the choice that makes the following statements true: 1. A rectangle is a parallelogram. A. Sometimes B. Always C. Never 2. A parallelogram is a rectangle. A. Sometimes B. Always C. Never 3. A rectangle is a square. A. Sometimes B. Always C. Never 4. A trapezoid is a parallelogram. A. Sometimes B. Always C. Never 5. A square is a rhombus. A. Sometimes B. Always C. Never 6. A rhombus is a square. A. Sometimes B. Always C. Never 7. A kite is a trapezoid. A. Sometimes B. Always C. Never 8. A rhombus is a rectangle. A. Sometimes B. Always C. Never Circle ALL of the choices that could make the following statements true: 9. 10. 11. 12. 13. A quadrilateral with exactly four congruent (equal) sides. A quadrilateral with exactly four right angles. A quadrilateral with two sets of parallel sides. A quadrilateral with exactly one set of parallel sides. A quadrilateral with two different sets of opposite, congruent sides. Square Trapezoid Rhombus Parallelogram Rectangle Kite Square Trapezoid Rhombus Parallelogram Rectangle Kite Square Trapezoid Rhombus Parallelogram Rectangle Kite Square Trapezoid Rhombus Parallelogram Rectangle Kite Square Trapezoid Rhombus Parallelogram Rectangle Kite 14. 15. 16. A quadrilateral with two different sets of adjacent, congruent sides. A quadrilateral with opposite sides congruent. A quadrilateral that does NOT have to contain right angles. Square Trapezoid Rhombus Parallelogram Rectangle Kite Square Trapezoid Rhombus Parallelogram Rectangle Kite Square Trapezoid Rhombus Parallelogram Rectangle Kite Square Trapezoid Rhombus Parallelogram Rectangle Kite Square Trapezoid Rhombus Parallelogram Rectangle Kite Square Trapezoid Rhombus Parallelogram Rectangle Kite Circle ALL of the choices that represent the following figures: 17. 18. 19. Circle ONE CHOICE that represents the BEST DESCRIPTION for each of the below figures (ONE choice): 20. Square Trapezoid Rhombus Parallelogram Rectangle Kite Square Trapezoid Rhombus Parallelogram Rectangle Kite Square Trapezoid Rhombus Parallelogram Rectangle Kite 21. 22.