14U. Let ABCD be a parallelogram. (a) Prove that ABCD is cyclic if and only if...
535 and 541
535. Suppose that ABCD is a parallelogram, in which AB- 2BC. Let M be the midpoint of segment AB. Prove that segments CM and DM bisect angles BCD and CDA, respectively. What is the size of angle CMD? Justify your response. from you toward the sun. How high is the sun in the sky? 541. Hexagon ABCDEF is regular. Prove that segments AE and ED are perpendicular. 549 Suppose that PORS is a rhombus with PO-12 and...
535 and 541
535. Suppose that ABCD is a parallelogram, in which AB- 2BC. Let M be the midpoint of segment AB. Prove that segments CM and DM bisect angles BCD and CDA, respectively. What is the size of angle CMD? Justify your response. from you toward the sun. How high is the sun in the sky? 541. Hexagon ABCDEF is regular. Prove that segments AE and ED are perpendicular. 549 Suppose that PORS is a rhombus with PO-12 and...
Problem 9. Let ABCD be a parallelogram. Let E be a point on AD. Let F = BEN AC and G = BE CD. Prove BF = V FG* FE
QUESTION 1
Quadrilateral WXZY is a square. If the measure of angle XYZ = 4x
+ 15, find the value of x.
15
15
18.75
7.5
2 points
QUESTION 2
Determine whether parallelogram JKLM with vertices J(-1, 1),
K(4, 1), L(4, 6) and M(-1, 6) is a rhombus, square, rectangle or
all three.
rhombus
square
rectangle
rhombus, square and rectangle
2 points
QUESTION 3
In rectangle JKLM, JK is equal to 12 feet, and LN is equal...
euclidean geometry
step by step process
1. (7 pts) Prove that the diagonals of a rectangle are congruent. 2. (18 pts) In the diagram below, prove that M is the midpoint of AC and BD if and only if ABCD is a parallelogram. 3. (9 pts) Use #1 and #2 above to prove that the diagonals of a square cut each other into 4 congruent segments. Use #3 to prove that the diagonals of a square are angle bisectors of...
prove the following
1)
2)
3)
4)A parallelogram is a square iff it's diagonals are
perpendicular and congruent.
5) the median of a trapeziod is parallel to each
base
3.7) Corollary (Parallel CT). Let l, and l be coplanar lines and I a transversal. a. (Property C) 4 | l, if and only if a pair of interior angles on the same side of t are supplementary b. (Property T) Ift 1 l and 41 || 12, then t 1...
prove this theorem
Theorem 10.25. Every parallelogram has the following properties. (a) Each diagonal cuts it into a pair of congruent triangles. (b) Both pairs of opposite sides are congruent. (C) Both pairs of opposite angles are congruent. (d) Its diagonals bisect each other.
(a) Let be a cyclic group of order . Prove that for every divisor of there is a subgroup of having order . (b) Characterize all factor groups of
4. Let ABCD be a rectangle with vertices A-(0,0), B 4,0) C(4,3), D (0,3) Suppose an isometry f: RR maps ABCD to a new rectangle PQRS where P-f(A)(2,4) and R- f(C)(2,9) Find all possible isometries f, and the remaining points Qf(B) and S-f(D) of the new rectangle.
(a) Let G be a cyclic group of order n. Prove that fo every divisor d of n there is a subgroup of G having order d. (b) Characterize all factor groups of Z70.