Geometry Unit 6 Answers PHS

(L1) Given: ▱ EFGHProve: EF¯≅GH¯; EH¯≅GF¯ : Statements-3: ∠1≅∠4; ∠2≅∠3Reasons-2: Def. of Parallelogram4: Reflexive Prop. of ≅5: ASA

(L1) Theorem 6.1C states that if a quadrilateral is a parallelogram, then its consecutive _____ are supplementary. : angles

(L1) Theorem 6.1B states that if a quadrilateral is a parallelogram, then its _____ angles are congruent. : opposite

(L1) Given: ▱ MNOPProve: MO¯ and NP¯ bisect each other at Q : Statements-4: MN¯≅OP¯5: ΔMNQ≅ΔOPQReasons-2: Def. of Parallelogram3: Alternate Interior Angles Theorem7: Def. of Midpoint

(L1) Refer to ▱ DEFGm∠DGF=113°What is m∠DEF? _____ : 113°

(L1)Refer to ▱ DEFGm∠DGF=113°m∠DEF+m∠EFG= _____ : 180°

(L2) Theorem 6.2A states: If one pair of opposite sides of a quadrilateral is both _____ and congruent, then the quadrilateral is a parallelogram. : parallel

(L2) Theorem 6.2B states: If both pairs of opposite _____ of a quadrilateral are congruent, then the quadrilateral is a parallelogram. : sides

(L2) Which quadrilateral shown could be proved to be a parallelogram by Theorem 6.2B (Quad with opp. sides ▱≅→▱ )? : ABCD

(L2) Which quadrilateral shown could be proved to be a parallelogram by Theorem 6.2C (Quad with opp. ▱∠s≅→▱ )? : QRST

(Q1) Refer to ▱ KLMNKP= _____ : MP

(Q1) Refer to ▱ KLMNm∠1+m∠2= _____ : 180°

(Q1) Refer to ▱ KLMNWhat is the length of MN¯ in cm? : 6 cm (?)

(Q1) Refer to ▱ KLMNKL¯≅ _____ : MN¯

(Q1) Refer to ▱ KLMNWhat is the length of LM¯ in cm? _____ : 6 cm

(Q1) If a quadrilateral is a parallelogram, then its _____ bisect each other. : diagonals

(L3) Given: ABCD is a rectangle.Prove: ABCD is a parallelogram. : Reasons-2: Def. of Rectangle3: Rt. ∠≅ Theorem

(L3) Given: ABCD is a rectangle.Prove: AC¯≅BD¯ : Reasons-4: Reflexive Prop. of ≅5: Def. of rectangle7: SAS8: CPCTC

(L3) A _____ is a quadrilateral with four right angles. : rectangle

(L3) Theorem 6.3E states that if two congruent angles are _____, then each angle is a right angle. : supplementary

(L4) Given: ABCD is a rhombus.Prove: AC¯⊥BD¯ : Statements-6: . ΔBPC≅ΔCPDReasons-3: Def. of rhombus5: Reflexive Property of ≅7: CPCTC9. Linear Pair Thrm.11. Def. Right Angles

(L4) Complete this informal proof.MNOP is a rhombus (Given).MN¯≅MP¯; NO¯≅PO¯ (Def. of __________)MO¯≅ __________ (Reflexive Prop. of ≅)∆MNO≅∆MPO (__________)∠1≅∠2; ∠3≅∠4 (__________)MO¯ bisects ∠NMP and ∠NOP (Def. of __________)NO¯≅NM¯; PO¯≅PM¯ (Def. of __________)NP¯≅ __________ (Reflexive Prop. of ≅ )∆PMN≅∆ __________ (SSS)∠5≅∠6; ∠7≅∠8 (__________)NP¯ bisects ∠MNO and ∠MPO (Def. of __________). : Complete this informal proof.MNOP is a rhombus (Given).MN¯≅MP¯; NO¯≅PO¯ (Def. of rhombus)MO¯≅ MO (Reflexive Prop. of ≅)∆MNO≅∆MPO (SSS)∠1≅∠2; ∠3≅∠4 (CPCTC)MO¯ bisects ∠NMP and ∠NOP (Def. of bisect)NO¯≅NM¯; PO¯≅PM¯ (Def. of rhombus)NP¯≅ NP (Reflexive Prop. of ≅ )∆PMN≅∆ PON (SSS)∠5≅∠6; ∠7≅∠8 (CPCTC)NP¯ bisects ∠MNO and ∠MPO (Def. of bisect).

(L4) Theorem 6.4E states: If the diagonals of a parallelogram are _____, then the parallelogram is a rhombus. : perpendicular

(L4) A rhombus is a quadrilateral with four congruent _____. : sides

(L4) Given: WXYZ is a parallelogram; XZ¯⊥WY¯Prove: WXYZ is a rhombus. : Statements-9: ΔWPX≅ΔYPX11: WXYZ is a rhombusReasons-4: Def. right angle6: Reflexive Property of ≅

(L4) Given: ∠ABC is a rt. ∠; AC¯≅BD¯Yes or no, must the parallelogram be a square? __________ □ABC is a rectangle. Theorem __________ AC¯≅BD¯ Theorem __________ : Given: ∠ABC is a rt. ∠; AC¯≅BD¯Yes or no, must the parallelogram be a square? No□ABC is a rectangle. Theorem 6.3CAC¯≅BD¯ Theorem 6.3D

(L5) The _____ of a trapezoid is each of the parallel sides of a trapezoid. : base

(L5) The base _____ of a trapezoid are two consecutive _____ of a trapezoid whose common side is the base. : angles; angles

(L5) The Trapezoid Midsegments Theorem states that the midsegment of a trapezoid is __________ to each base and its length is one half the __________ of the lengths of both bases. : parallel; sum

(L5) Theorem 6.5E states that if a quadrilateral is an isosceles trapezoid, then the angles in each pair of base angles are _____. : congruent

(L5) Theorem 6.5B states that if a quadrilateral is a kite, then its diagonals are _____. : perpendicular

(L5) Given: trapezoid ABCD with midsegment EF¯;EF¯||AD¯;EF¯||BC¯Prove: EF=12(AD+BC)AD=(8-0)2+(0-0)2= __________BC=(6-2)2+(6-6)2= __________EF=(7-1)2+(3-3)2= __________12(AD+BC)=12(__________ + __________) = __________Does EF=12(AD+BC)? __________ : Given: trapezoid ABCD with midsegment EF¯;EF¯||AD¯;EF¯||BC¯Prove: EF=12(AD+BC)AD=(8-0)2+(0-0)2= __________ [7]BC=(6-2)2+(6-6)2= __________ [5]EF=(7-1)2+(3-3)2= 6 12(AD+BC)=12(__________ + 4) = __________ [4] [8]Does EF=12(AD+BC)? Yes

(Q2) Given: ∠GHI is a rt. ∠; ∠1=∠2; ∠3=∠4Is the parallelogram a square?▱▱GHIJ is a rectangle.▱▱GHIJ is a rhombus. : (3/10)Given: ∠GHI is a rt. ∠; ∠1=∠2; ∠3=∠4Is the parallelogram a square?▱▱GHIJ is a rectangle. Theorem 6.3C▱▱GHIJ is a rhombus. Theorem 6.3D

(Q2) Given: KM¯≅JL¯;∠1=∠2;∠3=∠4Is the parallelogram a square?▱▱JKLM is a rectangle.▱▱JKLM is a rhombus. : (6/10)Given: KM¯≅JL¯;∠1=∠2;∠3=∠4Is the parallelogram a square? Yes▱▱JKLM is a rectangle. Theorem 6.3C▱▱JKLM is a rhombus. Theorem 6.4F

(Q2) A square could be called a _____ since it has four congruent sides. : rhombus

(Q2) Given: AC¯≅BD¯Is the parallelogram a square?Write the number of the theorem that supports your answer: : (5/10) Given: AC¯≅BD¯Is the parallelogram a square? NoWrite the number of the theorem that supports your answer: AC¯≅BD¯ Theorem 6.3C

(L6) Find the area of the trapezoid to the nearest whole square cm.A= _____ : Find the area of the trapezoid to the nearest whole square cm.A= 14 cm 2

(L6) The _____ is the sum of the lengths of the sides of a closed plane figure. : perimeter

(L6) Area could be described as the number of _____ of a particular size that fit within the perimeter of a two dimensional figure. : squares

(L6) Area of a kite: _____ : A=1/2d¹d²

(L6) Perimeter of a triangle: _____ : P=a+b+c

(L6) Perimeter of a square: _____ : P=4s

(L6) Perimeter of a trapezoid: _____ : P=a+b+c+d

(L7) The _____ of a regular polygon is a point equidistant from each of its vertices. : center

(L7) Sometimes, the area of a composite figure can be found by _____ the areas of the shapes it contains together. : adding

(L7) Sometimes, the area of a composite figure can be found by _____ an area from the area of a simple shape. : subtracting

(Q3) Find the total area. (hexagon);(ap.=2.6cm);(side=3cm)A= _____ : Find the total area. (ap.=2.6cm);(side=3cm)A= 25.2 cm²

(Q3) Find the total area. (Decagon)A= _____ : Find the total area.A= 19cm²

(Q3) Perimeter is the _____ around a closed plane figure. : distance

(Q3) The area is the number of nonoverlapping _____ units that exactly cover a closed plane figure. : square

(Q3) The perimeter is the _____ of the lengths of the sides of a closed plane figure. : sum

(Q3) Find the perimeter of the rhombus.P= _____ : Find the perimeter of the rhombus.P= 13.2 cm

(PT) A quadrilateral is a polygon with ____ sides. : ...

(PT) The _____ is the perpendicular distance from the center of a regular polygon to any one of its sides. : ...

(PT) The diagonals of a _____ are both congruent and perpendicular. : ...

(PT) Find the area of the trapezoid.A= _____ : ...

(PT) Refer to Theorems 6.3B-D and 6.4B-F in your GPM.Given: AC¯≅BD¯;AC¯⊥BD¯Is the parallelogram a square?Write the number of the theorems that support your answer.AC¯≅BD¯ TheoremAC¯⊥BD¯ Theorem : ...

(PT) Find the perimeter.P= _____ : ...

(PT) Find the area of region 3 of the composite figure to the nearest tenth.A₃= _____ : ...

(PT) A parallelogram is a convex quadrilateral in which both pairs of opposite _____ are parallel. : ...