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Squares, Rectangles, and Rhombi! Questions from McDougal Littell, Geometry, 2007.

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Squares, Rectangles, and Rhombi Statements and Converses One Big FigureRectangles and Rhombi Grab Bag Review! Bonus Question: 5000 pts

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Topic 1: 200 Question: Is the statement true? What about its converse? – If a quadrilateral is a rectangle, then it is a parallelogram. Answer – A rectangle is always a parallelogram, but a parallelogram isn’t necessarily a rectangle.

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Topic 1: 400 Question: Is the statement true? What about its converse? – If a quadrilateral is a parallelogram, then it is a rhombus. Answer – A parallelogram isn’t necessarily a rhombus, but a rhombus is always a parallelogram.

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Topic 1: 600 Question: Is the statement true? What about its converse? – If a quadrilateral is a square, then it is a rhombus. Answer – A square is also a rhombus, but a rhombus isn’t necessarily a square.

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Topic 1: 800 Question: Is the statement true? What about its converse? – If a quadrilateral is a rectangle, then it is a rhombus. Answer – A rectangle isn’t necessarily a rhombus, and a rhombus isn’t necessarily a rectangle.

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Topic 1: 1000 Question: – If a statement and its converse are true, how can you make a new statement which incorporates both? Answer – If a statement and its converse are both true, then it is a biconditional statement. You can reword it into an “if and only if” statement to show that both “sides” hold.

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Topic 2: 200 Question: – BGED is a rectangle and ABCD is a rhombus, find the measure of ∠ GDB Answer – m ∠ GDB = 27˚

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Topic 2: 400 Question: – BGED is a rectangle and ABCD is a rhombus, find the measure of ∠ ABC Answer – m ∠ ABC = 54˚

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Topic 2: 600 Question: – BGED is a rectangle and ABCD is a rhombus, find the measure of ∠ DAB Answer – m ∠ DAB = 126˚

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Topic 2: 800 Question: – BGED is a rectangle and ABCD is a rhombus, find the measure of ∠ GCE Answer – m ∠ GCE = 126˚

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Topic 2: 1000 Question: – BGED is a rectangle and ABCD is a rhombus. List all of the triangles which are congruent in the figure. Answer – ΔABH, ΔADH, ΔCHD, ΔCBH, and the bottom triangles with hypotenuses of CG and CE are all congruent.

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Topic 3: 200 Question: – Find m ∠ URV Answer – m ∠ URV = 71˚

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Topic 3: 400 Question: – Find the length of RT. Answer – Length RT = 28.65

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Topic 3: 600 Question: – Find m ∠ RVT Answer – m ∠ RVT = 38˚

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Topic 3: 800 Question: – Find m ∠ XWO Answer – m ∠ XWO = 34˚

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Topic 3: 1000 Question: – Find the length of WZ. Answer – Length WZ = 18.45

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Topic 4: 200 Question: – Classify the quadrilateral and then solve for ‘x’ and ‘y’. Answer – The quadrilaterals is a square, while x = 4 and y = 9.

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Topic 4: 400 Question: – Classify the quadrilateral, and then solve for ‘x’ and ‘y’. Answer – The figure is a rhombus, while x = 5 and y = 11.

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Topic 4: 600 Question: – Draw the figure, and then solve Answer – Length XY = 11

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Topic 4: 800 Question: – Draw the figure and then solve. Answer – m ∠ Y = 60˚

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Topic 4: 1000 Question: – Draw the figure and then solve. Answer – Length WY = 10

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Topic 5: 200 Question: Answer – The slope of MN is (3/11) and PQ is (3/11), while the slope of MQ is (-5/4) and NP is (-5/4), so there are two pairs of parallel sides, so the MNPQ is a parallelogram.

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Topic 5: 400 Question: Answer – The distances of MN and PQ are 11.4, while the distances of NP and MQ are 6.4, so there are two pairs of congruent sides, meaning MNPQ must be a parallelogram.

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Topic 5: 600 Question: Answer – Because the diagonals are bisected, set 12x + 1 = 49 and 8y + 4 = 36. This gives x = 4 and y = 4.

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Topic 5: 800 Question: Answer – Let x = the first angle, and y = the adjacent angle. Recognize that x = 3y – 12 and y = 180 – x. Plugging in, one gets x = 132, so y = 48. One of the other interior angles is also 132, and another is 48.

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Topic 5: 1000 Question: Answer – The polygon has 5 sides; the interior angles sum to 540, and as always, the exterior angles sum to 360.

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Bonus Question: 5000 pts. Question: – Can claim that JANE is a more specific type of quadrilateral? Explain. Answer – Because JANE is a parallelogram, we already know its opposite sides are congruent. To show the angles of JANE are all 90, note that because JXPE is a parallelogram and XP is perpendicular to EN, PX is also perpendicular to JA. This implies that m ∠ PEA, m ∠ XJE, m ∠ PNA, and m ∠ XAN are all 90˚ because of alternate interior angles. Thus, JANE is a rectangle.

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Write down how much money you are willing to risk. If you get the question right, you win that money; if you get it wrong you lose it!

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Write down how much money you are willing to risk. If you get the question right, you win that money; if you get it wrong you lose it!

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