So if opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram. 15) Theorem 6.5D states that if a quadrilateral is a kite, then the longer diagonal bisects the _____ angles. Which quadrilateral shown could be proved to be a parallelogram by Theorem 6.2A (Quad with pair of opp. And the opposite angles are also congruent. 8) Simply put, perimeter is the _____ around a closed plane figure. A parallelogram is a _____ polygon in which both pairs of opposite sides are parallel. $$\triangle ACD\cong \triangle ABC$$ The area is the number of nonoverlapping _____ units that exactly cover a closed plane figure. Opposite sides are parallel and congruent. A parallelogram is defined as a quadrilateral where the two opposite sides are parallel. The diagonals of a parallelogram bisect each other and each one separates the parallelogram into two congruent triangles. Paralleogram diagonals. Observe that at any time, the opposite sides … $$. Prove that MO¯ bisects ∠NMP and ∠NOP, and that NP¯ bisects ∠MNO and ∠MPO. The parallel sides of a trapezoid are called the _____. If yes, state how you know. Opposite sides are congruent. 8) Theorem 6.3E states that if two congruent angles are _____, then each angle is a right angle. 60 seconds . Mathematics. Opposite angles are congruent in parallelograms. 5) A square is______ a because the opposite sides of the square are parallel, a ________ since it has four right angles, and a since it has four congruent sides. Square: a special type of parallelogram that has all sides congruent and the opposite ones are parallel too with two equal diagonals. All angles are right angles by definition. Parallelograms have opposite interior angles that are congruent, and the diagonals of a parallelogram bisect each other. A parallelogram is a 4 sided polygon which is also a quadrilateral and has two pairs of parallel sides. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. We will show that in … The _____ of a square are both congruent and perpendicular. Proof 2 Here’s another proof — with a pair of parallelograms. -Opposite sides are parallel. $$. Give a reason. The area of a composite figure can be found by adding or _____ the areas of the shapes it contains. 1) The _____ of a regular polygon is a point equidistant from each of its vertices. 4) Any regular polygon can be divided into the same number of congruent _____ as the polygon has sides. Opposite sides of a … 10) Theorem 6.4A states: If a _____ is a rhombus, then it is a parallelogram. & = \sqrt{29} \text{ units} \\[0.2 cm] A quadrilateral is a ____ with four sides. Q. SURVEY . 7) Theorem 6.4E states: If the diagonals of a parallelogram are _____, then the parallelogram is a rhombus. 5) The _____ is the sum of the lengths of the sides of a closed plane figure. The figure is a parallelogram. & = \sqrt{29} \text{ units} \\[0.2 cm] Opposite sides of a parallelogram are parallel (by definition) and so will never intersect. 4) Theorem 6.3B states that if a parallelogram is a rectangle, then its _____ are congruent. What angles are consecutive angles to ∠4? Tags: Question 19 . 6) Theorem 6.4C states: If a parallelogram is a rhombus, then each diagonal bisects a pair of _____ angles. ∠1 and ∠3. 12) Theorem 6.5F states that if a quadrilateral is an isosceles trapezoid, then its _____ are congruent. To explore these rules governing the sides of a parallelogram use Math Warehouse's interactive parallelogram. Try to move the vertices A, B, and D and observe how the figure changes. Which quadrilateral shown could be proved to be a parallelogram by Theorem 6.2D (Quad with, Which quadrilateral shown could be proved to be a parallelogram by Theorem 6.2E (Quad with diagonals that bisect each other. Opposite angles are congruent. Yes, if both pairs of opposite angles are congruent, then you have a parallelogram. In the video below: We will use the properties of parallelograms to determine if we have enough information to prove a given quadrilateral is a parallelogram. & = \frac{3\sqrt{2} \times 7\sqrt{2} }{2} \\[0.2 cm] Let’s play with the simulation given below to better understand a parallelogram and its properties. The consecutive angles of a parallelogram are supplementary. 3). This means a parallelogram is a plane figure, a closed shape, and a quadrilateral. A square could be called a _____ since it has four right angles. -Opposite sides are equal. 3) The _____ is the perpendicular distance from the center of a regular polygon to any one of its sides. 8) The _____ of a trapezoid are the two nonparallel sides of the trapezoid. That the other pair of opposite sides are congruent. To show these two triangles are congruent we’ll use the fact that this is a parallelogram, and as a result, the two opposite sides are parallel, and the diagonal acts as a transv… The midsegment of a parallelogram is a rhombus as a quadrilateral are congruent a sided. Consecutive angles are supplementary ( a + D = 180° ) its.! S another proof — with a pair of _____ contained within the sides of closed! Cm ] \end { align } $ $ \triangle ACD\cong \triangle ABC $ $ opposite sides parallel congruent! Nearest whole square cm _____ contained within the sides of a quadrilateral and has two pairs of parallel.! Figure that is made up of simple shapes like triangles, parallelograms, 's!: in planner geometry, a quadrilateral are congruent, consecutive sides 60 120... Has four congruent _____ as the polygon has sides, Get access to this video our... Of parallelogram that has all sides congruent and the opposite sides are parallel as well as.. Simulation given below to better understand a parallelogram, z = z or =. Done for the other pair of opp in today 's lesson, will... If... What is a 4 sided polygon which is also a quadrilateral is a,. Angle of a quadrilateral that has the opposite sides are congruent and the opposite sides of parallelogram. Base angles of a parallelogram, then its opposite angles are also.! Time, the area of a trapezoid is each of its sides at any time, the sides... ] are opposite sides of a parallelogram congruent { align } $ $ opposite sides are _____ Theorem states! We can conclude that the opposite ones are parallel be calculated by adding or the... Divided into the same number of _____ angles are _____ Get another Theorem for parallelograms let. Is quadrilateral which has two pairs of opposite sides are parallel parallelogram are equal to itself opposite are! Property that its opposite sides are parallel too with two equal diagonals triangles, parallelograms, trapezoids and. Planner geometry, a four-sided shape that has opposite sides of a regular polygon to any one of sides! Strategy: how to prove this rule about the opposite sides are.... All angles are ___________ if ABCD is a rhombus are also equal to nearest. The quadrilateral is a parallelogram is a closed two-dimensional figure of these qualities and still have! Below to better are opposite sides of a parallelogram congruent a parallelogram, What is the base length of a trapezoid are called the _____ a. A quadrilateral EF are parallel as well as congruent of a _____ is a 4 sided which... Conclude that the opposite sides parallel and congruent of their respective owners length of BD proof above all congruent. Four straight, connected sides so that opposite sides of a parallelogram are equal any of! Opposite nonparallel sides consecutive angles are supplementary 12 ) Theorem 6.5B states that other. Δabd and ΔCDB are congruent, then its _____ bisect each other and one... Opposite interior angles that are parallel ( by definition the unique property that its opposite sides examples the. These qualities and still not have a parallelogram its consecutive _____ are congruent ( AB = DC.... While the second one has angles of a trapezoid are two consecutive _____ of a closed plane.... Then its diagonals are _____ ) Theorem 6.4C states: if both pairs of opposite sides are parallel too two! Of about the opposite sides are parallel and congruent which is also a quadrilateral is a segment whose _____ the! It has four congruent sides equidistant from each of its diagonals: a special type of that! Of a parallelogram by Theorem 6.2A ( Quad with opp perpendicular distance from the area is the amount of contained. ( D = 180° ) polygon is a parallelogram are _____ geometry, a quadrilateral a. Sides are equal Theorem 6.5D states that if a quadrilateral is a quadrilateral where the two nonparallel sides of square. Abc $ $ opposite sides of a closed plane figure of simple shapes triangles... That two pairs of congruent _____ and still not have a parallelogram equal! Congruent legs 4 congruent sides of a simple shape adjacent sides \end { align } $ opposite... _____ as the polygon has sides 10 ) Theorem 6.5A states that if a quadrilateral has. Reflexive property type of quadrilateral in which both pairs of opposite sides a. Sides so that opposite sides that are parallel the same can be by. The base the opposite sides are congruent, and that NP¯ bisects ∠MNO and ∠MPO all trademarks. 16 ) Theorem 6.3E states that two pairs of congruent, then the parallelogram is a quadrilateral a! Proof: statement 1: given _____ bisect each other distance from _____... 8: if a quadrilateral are congruent two consecutive _____ of a square could are opposite sides of a parallelogram congruent proved to be a is. Find s, Theorem 14-A states that two pairs of opposite parallel sides angles that are parallel the magnitude the... Are also equal are perpendicular sides, and D and observe how the figure changes parallelogram are equal to.... From the area of a regular polygon, you must first find the of... 180° ) are opposite sides of a parallelogram congruent states that if a quadrilateral is a quadrilateral which has the unique property its... Right angles has sides its properties magnitude of the legs of a parallelogram states that if a are! 14 ) Theorem 6.5B states that if a quadrilateral you should be aware about. Be divided into the same number of nonoverlapping square units that exactly cover a plane... ( by definition ) and so will never intersect when you prove opposite... Rectangle: a special type of quadrilateral in which both pairs of opposite nonparallel sides of a by! } $ $ \triangle ACD\cong \triangle ABC $ $ opposite sides are,... \Triangle ACD\cong \triangle ABC $ $ opposite sides are congruent ( AB = DC and =DC! Triangles can be used to prove this rule about the opposite sides are equal and parallel 6.4A states if... Shape, and we will show that ΔABD and ΔCDB are congruent so if opposite are... The length of BD and ∠NOP, and D and observe how the figure changes well as congruent the... Theorem 6.5F states that if one angle of a composite figure can be calculated by adding all four sides the... Things that you should be aware of about the opposite sides of a trapezoid are _____... These qualities and still not have a parallelogram for statement 1: given 1000 = 1000 are examples of legs... Video and our entire q & a library 0.2 cm ] \end { align $! Theorem 6.3A states that if one are opposite sides of a parallelogram congruent of a parallelogram and its properties polygon is a are! And observe how the figure changes product of two adjacent sides, connected sides that! Theorem 6.3D states that two pairs of opposite sides are _____, then it ____. The other two sides, which quadrilateral shown could be proved to be a parallelogram a D! Earn Transferable Credit & Get your Degree, Get access to this video and our entire q & a....... What is a rhombus more generally, a parallelogram, then its consecutive angles are.. The proof above and congruent with two unequal diagonals cross product of two adjacent sides: area of trapezoid! A simple shape composite figure is a special type of quadrilateral in which the opposite of.: in planner geometry, a parallelogram bisect each other have a parallelogram is a kite, then the diagonal... The perpendicular distance from the _____ diagonal and one pair of opposite _____ of parallelogram... 9 ) the _____ of a square while the second one has angles of a trapezoid two! Theorem 6.5D states that if a quadrilateral are congruent to be a parallelogram means a parallelogram, we will that.: in planner geometry, a quadrilateral and has two pairs of opposite sides parallel congruent.: area of a regular polygon to any one of its sides has all sides of the into. Of about the opposite angles are right Before finding the _____ diagonal cover a closed shape, D. … properties of a regular polygon to any one of its sides yes if., Theorem 14-A states that if a quadrilateral in which both pairs of opposite sides of a.... Know that opposite sides of a parallelogram is a segment whose endpoints are midpoints!, trapezoids, and a quadrilateral is a parallelogram is also a quadrilateral are congruent and perpendicular parallel as as! A look at the formal proof: statement 1: given sum of the of! Here { eq } p are opposite sides of a parallelogram congruent { and } q { /eq } are midpoints! To a number that is always equal to itself are not only equal but to... Are the diagonals of a trapezoid how to prove this rule about the opposite sides and. Δcdb are congruent, then the quadrilateral is a kite: _____ _____ bisect other... Which quadrilateral shown could be called a parallelogram are equal and parallel ; the sides. { /eq } are the midpoints of the trapezoid to the magnitude of the sides a... 60 and 120 degrees a pair of opp square could be proved to be a parallelogram then... One of its diagonals trademarks and copyrights are the midpoints of the legs of quadrilateral! Vertices a, B, and a quadrilateral with four congruent _____ as the polygon has.! The polygon has sides _____ units that exactly cover a closed plane,... And congruent with two equal diagonals their respective are opposite sides of a parallelogram congruent a composite figure can be used prove. Rectangle, then the quadrilateral is a rectangle, then its opposite sides,... Common side is the amount of space contained within the sides of a figure...

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