Mathematics, 25.08.2020 17:01 leahandmaryssa

Match each statement to the reasons given for the geometric proof. Given: ABCD is a parallelogram

Prove: Diagonals bisect each other(AE=CE and BE = DE

Match each statement to the reasons given for the geometric proof.

Given: ABCD is a parallelogram

Answers: 3

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Answers

Answer from: miaglory3828

5, 3, 1, 2, 6, 4

Step-by-step explanation:

The proof should be written as follows (which is a different order than provided):

Statement Reason

1. ABCD is a parallelogram 1. Given

2. AB||DC and AD||BC and AB ≅ DC 2. Definition of parallelogram

3. ∠ABD ≅ ∠CDB 3. Alternate Interior Angles Theorem

4. ∠DEC ≅ ∠BEA 4. Vertical Angles Theorem

5. ΔABE ≅ ΔCDE 5. AAS Congruency Theorem

6. AE = CE and BE = DE 6. CPCTC

This is the order provided in your question:

5. ΔABE ≅ ΔCDE 5. AAS Congruency Theorem

3. ∠ABD ≅ ∠CDB 3. Alternate Interior Angles Theorem

1. ABCD is a parallelogram 1. Given

2. AB||DC and AD||BC and AB ≅ DC 2. Definition of parallelogram

6. AE = CE and BE = DE 6. CPCTC

4. ∠DEC ≅ ∠BEA 4. Vertical Angles Theorem

Answer from: Quest

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

Answer from: Quest

Hello!

the answer is:

the correct option:

b. $x=2.23$

why?

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

$7^{x}=77$

then, using placing logarith with base 7 on both sides of the equation, we have:

$7^{x}=77log_{7}(7^{x})=log_{7}(77)x=log_{7}(77)x=2.2322$

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

$x=2.23$

hence, we have that the correct option:

b. $x=2.23$

have a nice day!

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Match each statement to the reasons given for the geometric proof. Given: ABCD is a parallelogram