Complete the proof for proving that the diagonals of an isosceles trapezoid are congruent 19 Given: Trapezoid EFGH with FE = GH F-b, c) G(b, c) Prove: EG = HF E(-a, 0) 01 H(a,0) Proof: By the Distance Formula, EG = a. ? and HF = b._? By the transitive property of congruence, EG = HF. Therefore, EG = HF by the definition of congruence. Fill in the blank for space a. Proof: By the Distance Formula, EG = a....
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
- AD is congruent to BC (diagonals are congruent)
- AB is parallel to CD
- angle SUT is less than pi/2
- RS is less than or equal to TU
2 Consider the following quadrilaterals in Neutal acome ky ㄗ 乃
Question 1. Prove the converse of the isosceles triangie theorem: if a triangle has two angles equal, then the sides opporite the oqual angles are equal
prove that a triangle is isosceles if and only if two altitudes are congruent. prove both ways
2. Prove Theorem 6.2.5: If the diagonals of a parallelogram are perpendic- ular, then the parallelogram is a rhombus. Specifically, given parallel- ogram PSRQ below with PR L QS, proe that PO QR RSSP.
W. X 3. Given: WXYZ with Diagonals WY and xz Prove: AWMX = AYMZ Z Y Statements Reasons 1. 1. Given 2. 2 Opposite sides of parallelogram are 3. 3. Vertical angles 4. 4. Diagonals of parallelogram 5. AWMX = AYMZ
Proof that: The line joining the midpoints of the diagonals of a trapezoid has length equal to half the difference of the bases.
please prove
Theorem 5.8 (Converse to the Isosceles Triangle Theorem). If two angles of a triangle are congruent to each other, then the sides opposite those angles are congruent.
3. (6 points) Consider the regular pentagon ABCDE with sides of length 1 and three diagonals as shown. Let the diagonals have length. The measure of each interior angle of a regular pentagon is 108° The isosceles triangles ABF and ECD are similar and each have angles 369-36° -1080 (a) Use a proportion for similar triangles ABF and ECD and the quadratic formula, -btVb2-4ac dc to show that x = * (the golden ratio). 2a * 360 x (diagonal) (b)...