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polet [3.4K]
3 years ago
7

Please answer quick! Thank You! Math

Mathematics
2 answers:
malfutka [58]3 years ago
5 0

Answer:

C and D.

Step-by-step explanation:

We are given that Spencer wrote a paragraph for proving that rectangles are parallelograms with congruent diagonals

We have to find the missing step in Spencer's proof

Proof:

According to the given information quadrilateral RECT is a rectangle. By definition of a rectangle , all four angles measure 90^{\circ}

.Segment ER is parallel to segment CT and segment EC is parallel to segment RT by the converse of the same- side Interior Angles Theorem.

Converse of the same- side angles theorem: When the sum of same side interior angles of a transversal line is180^{\circ} then the lines are parallel.

Quadrilateral RECT is then a parallelogram by definition of a parallelogram .Now, construct diagonals ET and CR. Because RECT is a parallelogram ,opposite sides are congruent.Therefore, one can say that segment ER is congruent to segment  CT.Segment TR is congruent to itself by the reflexive Property of equality.The Side-Angle-Side(SAS) Theorem says triangle ERT is congruent to triangle CTR.And because corresponding parts of congruent triangles are congruent (CPCTC),diagonals ET and Cr are congruent.

Answer :Option C and D

Converse of the same-Side Interior angles Theorem

Musya8 [376]3 years ago
4 0
I believe it is B.) Alternate Interior.
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Read 2 more answers
Given the following 2 equations, state whether these equations are parallel, perpendicular, or neither.
stiks02 [169]

Answer:

Neither

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The slope-intercept form of the equation of a line is generally given as;

y=mx+b

where m = the slope of the line

b = the y-intercept of the line

Two lines are said to be parallel if they have the same slope. Looking at the two given equations below, we see that the slope of the 1st one, 5/7, is different from the slope of the 2nd one, 7/5;

\begin{gathered} y=\frac{5}{7}x+14 \\ y=\frac{7}{5}x-20 \end{gathered}

Two lines are said to be perpendicular if their slopes are negative reciprocals of each other, let's go ahead and compare their slopes;

\begin{gathered} m_1=\frac{5}{7} \\ m_2=\frac{7}{5} \\ \therefore m_2=\frac{1}{m_1_{}} \end{gathered}

So the two lines are not perpendicular to each other. It, therefore, means that the correct answer will be Neither.

3 0
1 year ago
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