Presentation on theme: "By: Tyler Register and Tre Burse"— Presentation transcript:
1 By: Tyler Register and Tre Burse without 4.7Proving quadrilateral propertiesConditions for special quadrilateralsConstructing transformationsBy: Tyler RegisterandTre Bursegeometry
2 The Vocabulary and Theorems A diagonal of a parallelogram divides the parallelogram into two equal trianglesOpposite sides of a parallelogram are congruentOpposite angles of a parallelogram are congruentDiagonals of a parallelogram bisect each other
3 Theorems cont. A rhombus is a parallelogram A rectangle is a parallelogramThe diagonals and sides of a rhombus form 4 congruent trianglesThe diagonals of a rhombus are perpendicularThe diagonals of a rectangle are congruentA square is a rhombus
4 Theorems cont.The diagonals of a square are perpendicular and are bisectors of the anglesIf two pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogramIf the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram
5 TheoremsIf one angle of a parallelogram is a right angle then the parallelogram is a rectangleIf the diagonals of a parallelogram are congruent then the parallelogram is a rectangleIf one pair of adjacent sides of a quadrilateral are congruent then the quadrilateral is a rhombus
6 More TheoremsIf the diagonals of a parallelogram bisect the angles of the parallelogram then it is a rhombusIf the diagonals of a parallelogram are perpendicular than it is a rhombusTriangle mid-segment theorem- A mid-segment of a triangle is parallel to a side of the triangle and its length is equal to half the length of than side
7 The Last Theorem SlideBetweenness postulate- given the three points: P, Q, and R PQ+QR=PR then Q is between P and R on a line.The Triangle inequality theorem- The sum of any two sides of a triangle are greater than the other side.
8 4-5Statements ReasonsPLGM is a parallelogram and LM is a diagonalGivenDef of parallelogramObjective- Prove quadrilateral conjectures by using triangle congruence postulates and theorems.PL II GMGiven: parallelogram PLGM with diagonal LM< 3 = < 2Alt. Int. anglesPM II GLDef of parallelogramProve: triangle LGM= triangle MPL<1 = <4Alt. Int. anglesLM=LMreflexiveLGM= MPLASAP LM G
9 Conditions of special quadrilaterals 4-6Conditions of special quadrilateralsThere are many theorems in this section that state special cases in quadrilateralsThe most notable of these theorems is the House Builder TheoremThere is also the Triangle Mid- segment TheoremHouse Builder Theorem: If the diagonals of a parallelogram are congruent then the parallelogram is a rectangleTriangle Mid-segment Theorem: A mid-segment of a triangle is parallel to a side of the triangle and its length is equal to half the length of than sideThe list of the theorems in 4-6 are on page 5 and 6
10 4-8 Constructing transformations This section has one theorem and one postulateThe Betweenness postulate (converse of the segment addition postulate) and the Triangle Inequality TheoremThe Betweenness postulate: given the three points: P, Q, and R PQ+QR=PR then Q is between P and R on a line.Triangle Inequality Theorem: The sum of any two sides of a triangle are greater than the other side.5+7>XX+5>7X+7>52<X<1357X
11 Quiz Which of the following are possible lengths of a triangle? A. 14,8, B.16,7, C.18,8,24If one angle of a quadrilateral is a right angle than the quadrilateral is a ___________.Find the measure of the following angles:<Q=<RPQ=<PRQ=Rectangle60P QS R40806040
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