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Geometry--Ch. 6 Review

1). 2). Geometry--Ch. 6 Review. Classify each polygon as regular/irregular, concave/convex, and name it based on its number of sides:. irregular concave decagon. regular convex pentagon. 148 o. 108 o. x o. 112 o. 87 o. x = 85 o. Geometry--Ch. 6 Review. 3) Find the value of x:.

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Geometry--Ch. 6 Review

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  1. 1) 2) Geometry--Ch. 6 Review Classify each polygon as regular/irregular, concave/convex,and name it based on its number of sides: irregularconcavedecagon regularconvexpentagon

  2. 148o 108o xo 112o 87o x = 85o Geometry--Ch. 6 Review 3) Find the value of x: Since the figure is a pentagon,the interior angle sum must be 540o. Angle Sum = (5-2)(180) = 540o These four angles add up to 455o. x = 540 - 455

  3. 128o 4x-3o 3x+20o 116o 4xo These angles add up to 362o. 118o Therefore, the remaining angles must add up to 358o. x = 31 Geometry--Ch. 6 Review 4) Find the value of x: Since the figure is a hexagon,the interior angle sum is 720o. (4x-3) + (3x+20) + 4x = 358 11x + 17 = 358 11x = 341

  4. Geometry--Ch. 6 Review 5) Find the interior angle sum for a convex septagon: ANSWER:Since a septagon has seven sides, we insert a 7 into the interior angle sum formula. Angle Sum = (n - 2)(180) Angle Sum = (7-2)(180) Angle Sum = (5)(180) 900 degrees

  5. 1080 - 969 = 111 Geometry--Ch. 6 Review 6) The sum of the measures of six angles in a convex octagon is 969o. The 7th angle is twice as large as the 8th angle. Find the measures of both missing angles: ANSWER:Since an octagon has eight sides, we know that the sum of its interior angles should be 1080 degrees. Angle Sum = (8-2)(180) = 1080 Since six of the angles add up to 969 degrees, the remaining two angles must add up to 111 degrees.

  6. 7th angle 8th angle 8th angle 7th angle 7th angle 8th angle 37o 74o (37) 2(37) x 2x Geometry--Ch. 6 Review 6) The sum of the measures of six angles in a convex octagon is 969o. The 7th angle is twice as large as the 8th angle. Find the measures of both missing angles: The remaining 111o must be divided into 3 equal parts. The reason for this is because one angle is twice as large as the other. + = 111 3x= 111 x= 37

  7. Geometry--Ch. 6 Review 7) A regular convex polygon has 12 sides. Find the measure of each interior angle and each exterior angle: ANSWER:Since the exterior angles always have to add up to 360, each exterior angle would have to be... 360/12 =30o Since the interior and exterior angles always combine to form linear pairs, each interior angle would have to be... 180 - 30 =150o

  8. Geometry--Ch. 6 Review 8) Each interior angle of a regular convex polygon measures 144 degrees. How many sides does the polygon have? ANSWER:If each interior angle is 144 degrees, then each exterior angle would have to be 36 degrees. 180 - 144 = 36 If each exterior angle is 36 degrees, then the polygon is a decagon with 10 sides. 360/36 = 10 sides

  9. 14 cm 14 cm 14 cm From last chapter, we know the length of the altitude is 7 3 . 14 cm Area = (½)(14)( 7 3 ) Area = 49 3 7 3 cm2 7 cm Geometry--Ch. 6 Review 9) Find the area of an equilateral triangle with sides of 14 cm: ANSWER:If you drop an altitude down from the vertex angle, two 30/60/90 triangles are formed.

  10. Geometry--Ch. 6 Review 10) Name the four properties of all parallelograms: ~Both pairs of opposite sides are congruent. ~Both pairs of opposite angles are congruent. ~Consecutive angles are supplementary. ~Diagonals bisect each other.

  11. 3x+4 6y+8o 11y+1o 5x-9 If x = 6.5, then this angle would be 47o. Since consecutive angles must be supplementary,this angle would be 133o. Geometry--Ch. 6 Review 11) Find x and y in the parallelogram shown: Opposite sides must be congruent. 5x - 9 = 3x + 4 2x - 9 = 4 2x = 13 x = 6.5 11y + 1 = 133 11y = 132 y = 12

  12. 53o 2x+11o 2yo 3x+5o zo 43o 53o Geometry--Ch. 6 Review 12) Find x, y, and z in the parallelogram shown: Like all triangles, this one’sangles add up to 180o. Opposite angles must be ≅. 3x + 5 = 53 53 + 43 + 2y =180 3x = 48 x = 16 If x=16, then this angle is 43o. y = 42 2y = 84 In a parallelogram, alternate interior angles are ≅. z = 43

  13. 14) 13) 15) Geometry--Ch. 6 Review Do the following quadrilaterals have to be parallelograms? If so, why? YES; Both pairs ofopposite sides are ≅. NO; We need BOTH pairs of opposite angles to be ≅. YES; The same pairof opposite sides is parallel and ≅.

  14. 68o 2 5 1 56o 56o 56o 56o 4 68o 3 Geometry--Ch. 6 Review 16) Find the missing angles in the following rhombus: Opposite angles are ≅. Since consecutive angles are supplementary, these large angles are each 112o. In a rhombus, diagonals bisect the opposite angles. Therefore, both 112o angles get split into four different 56o angles.

  15. 9 units apart 15 2x+8 24 6x+3 33 8x+5 x = 3.5 Geometry--Ch. 6 Review 17) Given the following trapezoid and its midsegment, find the value of x: (2x+8) + (8x+5)= 2(6x+3) 10x+13 = 12x+6 13 = 2x+6 By plugging the x = 3.5back in, we can see thatwe’re correct. 7 = 2x

  16. G 107o 4 42o 42o E T 3 107o 31o 1 2 31o M Geometry--Ch. 6 Review 18) Find the missing angles in the following kite: Kites have one pair of opposite angles ≅. So angles T & E are both 107o. Since the angle sum of a triangleis 180o, m∠2 = 31o. The two triangles in the kiteare ≅ (by SSS). Therefore, weknow the other missing angles as well.

  17. Geometry--Ch. 6 Review TRUE or FALSE? 19) The diagonals of a rectangle are congruent. TRUE 20) The diagonals of a trapezoid bisect each other. FALSE 21) All rhombuses are squares. (The converse is true.) FALSE 22) All parallelograms are quadrilaterals. TRUE

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