Geometry (QUADRILATERAL PARALLELOGRAMS THEOREMS PART 2)
Theorem 4-14
If a diagonal is drawn in a parallelogram, then two congruent triangles are formed.
Match the following reasons with the statements given to create the proof.
1. DO = OB, AO = OC 2. <DOC = <AOB 3. Triangle COD congruent to Triangle AOB 4. <1 = <2, AB = DC 5. AB||DC 6. ABCD is a parallelogram 1. Given 2. If two sides = and ||, then a parallelogram. 3. SAS 4. CPCTE 5. If alternate interior angles =, then lines parallel. 6. Vertical angles are equal.
Match the reasons to the statements given.
1. Parallelogram ABCD 2. BT = TD 3. <1 = <2 4. BC||AD 5. <3 = <4 6. Triangle BET congruent to Triangle DFT 7. ET = TF 1. Given 2. 3. CPCTE 4. If lines parallel, then alternate interior angles are =. 5. 6. 7.
Which of the following are quadrilaterals?
A quadrilateral is a geometric figure with four sides. trapezoids rectangles squares parallelograms
parallelogram
A quadrilateral with both pairs of opposite sides parallel.
Which of the following reasons would complete the proof in lines 3 and 5? https://internationalvla.sooschools.com/media/g_geo_ccss_2016/4/page77a.gif
Definition of parallel.
Theorem 4-18
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Theorem 4-16
If two sides of a quadrilateral are equal and parallel, then the quadrilateral is a parallelogram.
Corollary 1
Opposite angles of a parallelogram are equal.
Corollary 2
Opposite sides of a parallelogram are equal.
Theorem 4- 15
The diagonals of a parallelogram bisect each other.
Corollary 3
Two parallel lines are equidistant throughout.
A parallelogram is __________________ a quadrilateral.
always
A quadrilateral is ___________ a parallelogram.
always
If a diagonal is drawn in a parallelogram, then two congruent triangles are ________ formed.
always
Review the image and two-column proof below. https://internationalvla.sooschools.com/media/g_geo_ccss_2016/4/page77c.gif Which of the following represents a valid reason for statement #2?
opposite sides of a parallelogram are equal.
The diagonal of a parallelogram ____________ creates alternate interior angles.
sometimes