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LekaFEV [45]
2 years ago
13

In , side is extended to point E. When connected to vertex A, segment is parallel to segment . In this construction, you are giv

en that bisects .
Prove:
Complete the paragraph proof.

A diagram of a triangle ABC. D is the midpoint of the base AC. A line connects BD. A dashed line AE and BE is drawn outside the triangle.

, since bisects and the two angles created on each side of the bisector at point B are equal. because of the corresponding angles theorem. because
. by the substitution property of equality. by the triangle proportionality theorem. If two angles in a triangle are congruent, the sides opposite the angles are congruent, so .
by the substitution property of equality.
Mathematics
1 answer:
givi [52]2 years ago
8 0
  1. Angle 1 is congruent to angle 2, since BD bisects <ABC and the two angles created on each side of the bisector at point B are equal.
  2. <2 ≅ <3 because of the corresponding angles theorem.
  3. <1 ≅ <4 because alternate angles are congruent if two parallel lines are cut by a transversal.
  4. <3 ≅ <4 by the substitution property of equality.
  5. AD/CD = EB/CB by the triangle proportionality theorem.
  6. If two angles in a triangle are congruent, the sides opposite the angles are congruent, so AE = EB.
  7. AD/CD = AB/CB by the substitution property of equality.

<h3>The properties of similar triangles.</h3>

In Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

<h3>What is the substitution property of equality?</h3>

The substitution property of equality states that assuming x, y, and z are three (3) quantities, and if x is equal to y (x = y) based on a rule and y is equal to z (y = z) by the same rule, then, x and z (x = y) are equal to each other by the same rule.

In this context, we can reasonably infer and logically deduce that the ratio of AD/CD is equal to AB/CB based on the substitution property of equality.

Read more on substitution property here: brainly.com/question/2459140

#SPJ1

Complete Question:

In ΔABC, side BC is extended to point E. When connected to vertex A, segment EA is parallel to segment BD. In this construction, you are given that BD bisects <ABC.

Prove: AD/CD = AB/CB.

Complete the paragraph proof.

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Please help with the attached question. Thanks
Mademuasel [1]

Answer:

Choice A) F(x) = 3\sqrt{x + 1}.

Step-by-step explanation:

What are the changes that would bring G(x) to F(x)?

  • Translate G(x) to the left by 1 unit, and
  • Stretch G(x) vertically (by a factor greater than 1.)

G(x) = \sqrt{x}. The choices of F(x) listed here are related to G(x):

  • Choice A) F(x) = 3\;G(x+1);
  • Choice B) F(x) = 3\;G(x-1);
  • Choice C) F(x) = -3\;G(x+1);
  • Choice D) F(x) = -3\;G(x-1).

The expression in the braces (for example x as in G(x)) is the independent variable.

To shift a function on a cartesian plane to the left by a units, add a to its independent variable. Think about how (x-a), which is to the left of x, will yield the same function value.

Conversely, to shift a function on a cartesian plane to the right by a units, subtract a from its independent variable.

For example, G(x+1) is 1 unit to the left of G(x). Conversely, G(x-1) is 1 unit to the right of G(x). The new function is to the left of G(x). Meaning that F(x) should should add 1 to (rather than subtract 1 from) the independent variable of G(x). That rules out choice B) and D).

  • Multiplying a function by a number that is greater than one will stretch its graph vertically.
  • Multiplying a function by a number that is between zero and one will compress its graph vertically.
  • Multiplying a function by a number that is between -1 and zero will flip its graph about the x-axis. Doing so will also compress the graph vertically.
  • Multiplying a function by a number that is less than -1 will flip its graph about the x-axis. Doing so will also stretch the graph vertically.

The graph of G(x) is stretched vertically. However, similarly to the graph of this graph G(x), the graph of F(x) increases as x increases. In other words, the graph of G(x) isn't flipped about the x-axis. G(x) should have been multiplied by a number that is greater than one. That rules out choice C) and D).

Overall, only choice A) meets the requirements.

Since the plot in the question also came with a couple of gridlines, see if the points (x, y)'s that are on the graph of F(x) fit into the expression y = F(x) = 3\sqrt{x - 1}.

5 0
3 years ago
Read 2 more answers
Write 108.92 in expanded form
Kitty [74]
Sorry if my writing is sloppy

5 0
3 years ago
Choose the slope and y-intercept that correspond with the graph. ​ignore this
krok68 [10]

Answer: The second choice is correct:  slope is 3/4, y-intercept is 1

Step-by-step explanation: The y-intercept is where the line crosses the y-axis.

Look for places where the line intersects the grid at "cross-points" like (-4,-2) (0,1) and (4,4)

The slope is rise/run.

The difference in y-values is the rise. 4-1=3  1-(-2) is 3.

The rise is 3.

The difference in x-values is the run. 4-0=4  0-(-4) = 4

The run is 4

Rise/run = 3/4  That is the slope.

8 0
3 years ago
Read 2 more answers
determine whether the lines intersect and if so find the point of intersection and the cosine of the angle of intersection x=4t+
Fittoniya [83]

Answer:

As the lines are not intersecting nor parallel, they must be skew.

Step-by-step explanation:

Question is incomplete, we consider the nearest match available online.

Parametric equations of two lines are:

L₁ : x=4t+2 , y = 3 , z =-t+1

L₂: x=2s+2 , y= 2s+5 , z = s+1

If lines are parallel then parametric coordinates must be equal scalar multiple of each other which s not true here.

4t+2=2s+2 ---(1)\\ \\3=2s+5---(2) \\\\-t+1=s+1---(3)

If lines are intersecting then parametric coordinates must be equal for some value of t and s.

From (3)\\-t=s\\From (2)\\\\s=\frac{3-5}{2}\\\\s=-1\\\implies t=1\\\\To\,\,check\,\, the \,\,values \,\,of \,\,s\,\, and \,\,t \,\,for\,\,intersection\,\,put \,\,them\,\, in\,\, (1)\\\\4(1)+2= 2(-1)+2\\ 6\ne0

Hence the lines are not intersecting nor parallel, they must be skew.

6 0
3 years ago
There are 16 females and 20 males at the park. Which of the following represents the probability of
meriva

Answer:

d. 20/36

Step-by-step explanation:

total: 36

males: 20

3 0
2 years ago
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