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2 years ago

9

Looking at the labeled information in the figure below, create a statement that details a pair of angles (not already labeled) t

hat are congruent because of corresponding parts of congruent
triangles
(Name the vertices in each angle in alphabetical order)
B
A
lion dose

1 answer:

Morgarella [4.7K]2 years ago

8 0

Answer:

In triangles ΔBAE and ΔCED, which are congruent triangles, ∠ DBA is congruent to ∠CDB because corresponding parts of congruent triangles are Congruent, (CPCTC)

Step-by-step explanation:

The given information are;

In triangle ΔBAE and ΔCED, ∠EAB Alternate angles)is congruent to ∠ECD (

∠CED is congruent to ∠AEB (Vertically opposite angles)

Segment $\overline {BA}$ is congruent to segment $\overline {DC}$ (Given)

Therefore;

Triangle ΔBAE is congruent to ΔCED (Angle Angle Side AAS congruency rule)

Therefore, ∠ DBA is congruent to ∠CDB (Corresponding Parts of Congruent Triangles are Congruent, (CPCTC))

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Use complete sentences to explain the relationship between tan 5pi/4 and tan pi/4. In your answer, reference specific values on

Kisachek [45]

Remark
pi/4 is between 0 and pi/2 which means that pi/4 is in the first quadrant.

5*pi / 4 is between pi and 3/2 pi which means that the angle is in the third quadrant.

So you are talking about one two angles that are in the first and third quadrants.

Step One
Find the Tangent of pi/4 using the unit circle as a reference.

Since pi/4 is 1/2 way between 0 and pi/2 you are referring to something that has and x value of 0.707 for an x value and 0.707 for a y value. (They are equal)

That is the point where the opposite / adjacent = 0.707/0.707 = 1

Step Two
Find the tangent of 5pi/4 using the unit circle.
Using the same argument as pi/4 this time the opposite / adjacent = -0.707/-0.707 = 1 ( the two minus signs cancel out.)

8 0

2 years ago

The team first experiments with changing the position of the curved pit. In the computer program, the

Tju [1.3M]

Answer:

1). Shifted 2 units right.

2). Shifted 2 units left.

3). Shifted 2 units up.

4). Shifted 2 units down.

Step-by-step explanation:

Parent quadratic function is,

y = x²

1). When curved pit of the parent function is shifted 2 units right,

Translated function will be,

y = (x - 2)²

2). The curved pit is shifted 2 units left,

y = (x + 2)²

3). The curved pit is shifted 2 units up,

y = x² + 2

4). The curved pit is shifted 2 units down,

y = x² - 2

6 0

2 years ago

The area of ABED is 49 square units. Given AGequals9 units and ACequals10 units, what fraction of the area of ACIG is represent

Mrac [35]

Answer:

The fraction of the area of ACIG represented by the shaped region is 7/18

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the square ABED find the length side of the square

we know that

AB=BE=ED=AD

The area of s square is

$A=b^{2}$

where b is the length side of the square

we have

$A=49\ units^2$

substitute

$49=b^{2}$

$b=7\ units$

therefore

$AB=BE=ED=AD=7\ units$

step 2

Find the area of ACIG

The area of rectangle ACIG is equal to

$A=(AC)(AG)$

substitute the given values

$A=(9)(10)=90\ units^2$

step 3

Find the area of shaded rectangle DEHG

The area of rectangle DEHG is equal to

$A=(DE)(DG)$

we have $DE=7\ units$

$DG=AG-AD=9-7=2\ units$

substitute $A=(7)(2)=14\ units^2$

step 4

Find the area of shaded rectangle BCFE

The area of rectangle BCFE is equal to

$A=(EF)(CF)$

we have

$EF=AC-AB=10-7=3\ units$

$CF=BE=7\ units$

substitute

$A=(3)(7)=21\ units^2$

step 5

sum the shaded areas

$14+21=35\ units^2$

step 6

Divide the area of of the shaded region by the area of ACIG

$\frac{35}{90}$

Simplify

Divide by 5 both numerator and denominator

$\frac{7}{18}$

therefore

The fraction of the area of ACIG represented by the shaped region is 7/18

5 0

2 years ago

The park shown is in the shape of a square. Is the perimeter rational or irrational? Area = 24,200 yd 2

dangina [55]

Answer:

irrational

Step-by-step explanation:

A = s^2

s^2 = 24,200

$s = \sqrt{24200}$

$s = \sqrt{242 \times 100}$

$s = \sqrt{100 \times 121 \times 2}$

$s = 10 \times 11\sqrt{2}$

$s = 110\sqrt{2}$

P = 4s

$P = 4 \times 100 \sqrt{2}$

$P = 440 \sqrt{2}$

The perimeter is irrational.

3 0

2 years ago

In the diagram, transversal t cuts across the parallel lines a and b. Match the pairs of angles with the relationship that shows

charle [14.2K]

we know that

<u>case a)</u> alternate exterior angles

m∠2=m∠7 --------> by alternate exterior angles

m∠1=m∠8 --------> by alternate exterior angles

<u>case b)</u> alternate interior angles

m∠3=m∠6 --------> by alternate interior angles

m∠5=m∠4 --------> by alternate interior angles

<u>case c)</u> corresponding angles

m∠1=m∠5 --------> by corresponding angles

m∠3=m∠7 --------> by corresponding angles

m∠2=m∠6 --------> by corresponding angles

m∠4=m∠8 --------> by corresponding angles

<u>case d)</u> vertical angles

m∠1=m∠4 --------> by vertical angles

m∠2=m∠3 --------> by vertical angles

m∠5=m∠8 --------> by vertical angles

m∠6=m∠7 --------> by vertical angles

therefore

the answer in the attached figure

5 0

2 years ago