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VMariaS [17]
2 years ago
9

Spencer wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals. Quadrilateral R

E C T is shown with right angles at each of the four corners. Segments E R and C T have single hash marks indicating they are congruent while segments E C and R T have two arrows indicating they are parallel. Segments E T and C R are drawn. According to the given information, quadrilateral RECT is a rectangle. By the definition of a rectangle, all four angles measure 90°. Segment ER is parallel to segment CT and segment EC is parallel to segment RT by the ________________. 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. Which of the following completes the proof? Alternate Interior Angles Theorem Converse of the Alternate Interior Angles Theorem Converse of the Same-Side Interior Angles Theorem Same-Side Interior Angles Theorem

Mathematics
2 answers:
katovenus [111]2 years ago
7 0

Answer:

The converse of the Same-Side Interior AnglesTheorem

Step-by-step explanation:

I just took the test and this was the right option, not the Same-side Interior Angles Theorem

Komok [63]2 years ago
6 0

We have to prove that rectangles are parallelograms with congruent Diagonals.

Solution:

1. ∠R=∠E=∠C=∠T=90°

2. ER= CT, EC ║RT

3.  Diagonals E T and C R are drawn.

4. Shows Quadrilateral R E CT is a Rectangle.→→[Because if in a Quadrilateral One pair of Opposite sides are equal and parallel and each of the interior angle is right angle than it is a Rectangle.]

5.  Quadrilateral RECT is a Parallelogram.→→[If in a Quadrilateral one pair of opposite sides are equal and parallel then it is a Parallelogram]

6. In Δ ERT and Δ CTR

(a) ER= CT→→[Opposite sides of parallelogram]

(b) ∠R + ∠T= 90° + 90°=180°→→→Because RECT is a rectangle, so ∠R=∠T=90°]

(c) Side TR is Common.

So, Δ ERT ≅ Δ CTR→→[SAS]

Diagonal ET= Diagonal CR →→→[CPCTC]

In step 6, while proving Δ E RT ≅ Δ CTR, we have used

(b) ∠R + ∠T= 90° + 90°=180°→→→Because RECT is a rectangle, so ∠R=∠T=90°]

Here we have used ,Option (D) : Same-Side Interior Angles Theorem, which states that Sum of interior angles on same side of Transversal is supplementary.

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A Biology student who created a regression model to use a bird's height when perched for predicting its wingspan made these two
VLD [36.1K]

Answer:

a) C

b) A

Step-by-step explanation:

The wingspan is the dependent variable while the bird height is the independent variable.

a) Since R2 is the dependent variable, it can be expressed by the independent variable. An R2 of 93% represents 93% of the variation in the wingspan which can be explained by using the birds height. This means that the appropriateness of the model should not be determined by R2 but by using a scatter plot.

b) The model predicts the value of wingspan using the value of bird height. We cannot say that the bird 10 inches tall has a wingspan if 17 inches instead, we say that the wingspan of the bird which is 10 inches tall is 17 inches.

It is therefore possible that the wing span is not exactly 17 inches

3 0
2 years ago
Find f(0), if not supplied, and then find the equation of the given linear function.
My name is Ann [436]

Answer:

Part 1) f(0)=2

Part 2) f(x)=3x+2

Step-by-step explanation:

Part 1) Find f(0)

we know that

Looking at the data in the table

When the value of x increases by 1 unit, the value of y increases by 3 units

therefore

When the value of x decreases by 1 unit from 1 to 0, the value of y would decreases 3 units from 5 to 2

thus

f(0)=2

This value represent the y-intercept

Part 2) Find the equation of the given linear

Find the slope

take the points (1,5) and (2,8)

m=(8-5)/(2-1)=3

The equation of the line in slope intercept form is equal to

f(x)=mx+b

we have

m=3\\b=2

substitute

f(x)=3x+2

3 0
3 years ago
Which set of numbers represents the lengths of the sides of a right triangle? 1. {7, 24, 25} 2. {9, 16, 23} 3. {10, 12, 14} 4. {
wolverine [178]
1
{7}^{2}  +  {24}^{2}  =  {25}^{2}
5 0
3 years ago
Show your work plzz :))))
ankoles [38]

Answer:

9/10

Step-by-step explanation:

1/6 hour for 3/20 of his yard

6/6 hour or 1 hour = 6* 3/20 = 9/10 of his yard per hour

Mark as brainliest if this helped

Mark as brainliest if this helped

6 0
2 years ago
Read 2 more answers
Various studies indicate that approximately 11% of the world's population is left handed. You think this number is actually high
Irina-Kira [14]

Answer:

a. H0 : p ≤ 0.11 Ha : p >0.11 ( one tailed test )

d. z= 1.3322

Step-by-step explanation:

We formulate our hypothesis as

a. H0 : p ≤ 0.11 Ha : p >0.11 ( one tailed test )

According to the given conditions

p`= 31/225= 0.1378

np`= 225 > 5

n q` = n (1-p`) = 225 ( 1- 31/225)= 193.995> 5

p = 0.4 x= 31 and n 225

c. Using the test statistic

z=  p`- p / √pq/n

d. Putting the values

z= 0.1378- 0.11/ √0.11*0.89/225

z= 0.1378- 0.11/ √0.0979/225

z= 0.1378- 0.11/ 0.02085

z= 1.3322

at 5% significance level the z- value is ± 1.645 for one tailed test

The calculated value falls in the critical region so we reject our null hypothesis H0 : p ≤ 0.11 and accept  Ha : p >0.11 and  conclude that the data indicates that the 11% of the world's population is left-handed.

The rejection region is attached.

The P- value is calculated by finding the corresponding value of the probability of z from the z - table and subtracting it from 1.

which appears to be 0.95 and subtracting from 1 gives 0.04998

8 0
3 years ago
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