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.
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 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
Answer the following questions 92-99 For questions 92 and 93, refer to parallelogram MNOP. 92. ZPMN LNOP a. True b. False 93. PM ON a. True b. False 94. If CDEF is a rectangle and CD = 6, what is EF? a. 12 b. 6 C. d. 2 95. If MNOP is a square, what is a. 180 b. 135 MNP? c. 90 d. 45 96. If ABCD is a trapezoid with bases of lengths 14 m and 8 m,...