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3 years ago

I don’t understand how to proof Cpctc or answer the questions

Mathematics

1 answer:

n200080 [17]3 years ago

4 0

I think that first you need to understand what CPCTC is used for.

Let's start with the definition of congruent triangles.

Definition of congruent triangles
Two triangles are congruent if each side of one triangle is congruent to a corresponding side of the other triangle and each angle of one triangle is congruent to a corresponding angle of the other triangle.

A definition works two ways.
1) If you are told the sides and angles of one triangle are congruent to the corresponding sides and angle of a second triangle, then you can conclude the triangles are congruent.
2) If you are told the triangles are congruent, then you can conclude 6 statements of congruence, 3 for sides and 3 for angles.

Now let's see what CPCTC is and how it works.
CPCTC stands for "corresponding parts of congruent triangles are congruent."
The way it works is this. You can prove triangles congruent by knowing fewer that 6 statements of congruence. You can use ASA, SAS, AAS, SSS, etc. Once you prove two triangles congruent, then by the definition of congruent triangles, there are 6 congruent statements. That is where CPCTC comes in. Once you prove the triangles congruent, then you can conclude two corresponding sides or two corresponding angles are congruent by CPCTC. These two corresponding parts were not involved in proving the triangles congruent.

Problem 1.

Statements Reasons
1. Seg. AD perp. seg. BC 1. Given
2. <ADB & <ADC are right angles 2. Def. of perp. lines
3. <ADB is congr. <ADC 3. All right angles are congruent
4. Seg. BD is congr. seg CD 4. Given
5. Seg. AD is congr. seg. AD 5. Congruence of segments is reflexive
6. Tr. ABD is congr. tr. ACD 6. SAS
7. Seg. AB is congr. seg. AC 7. CPCTC

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How do you solve 8|x+2|-6=5|x+2|+3

sergejj [24]

Answer:

x = 1 or x = -5

Step-by-step explanation:

Solve for x over the integers:

8 abs(x + 2) - 6 = 5 abs(x + 2) + 3

Subtract 5 abs(x + 2) - 6 from both sides:

3 abs(x + 2) = 9

Divide both sides by 3:

abs(x + 2) = 3

Split the equation into two possible cases:

x + 2 = 3 or x + 2 = -3

Subtract 2 from both sides:

x = 1 or x + 2 = -3

Subtract 2 from both sides:

Answer: x = 1 or x = -5

7 0

3 years ago

Straight angles Are extremely important in geometry. When two lines intersect , they form multiple angles. In the diagram below,

rusak2 [61]

When two straight lines intersect, the vertical opposite angles intersect. the other two angles are also equal. Let the known angle be x, then the other two adjacent angles are obtained subtracting twice of x from 360 and dividing the result by 2.

Therefore, the table can by filled as follows:

Row 1:

Given <GEF = 120°

<FEM is adjacent to <GEF, thus
$\angle FEM= \frac{360-2(120)}{2} \\ \\ = \frac{360-240}{2} = \frac{120}{2} =60^o$

<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <MEH = 120°

<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <HEG = 60°.

Row 2:

Given <MEH = 150°

<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <GEF = 150°

<FEM is adjacent to <GEF, thus
$\angle GEF= \frac{360-2(25)}{2} \\ \\ = \frac{360-50}{2} = \frac{310}{2} =155^o$

<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <HEG = 30°.

Row 3:

Given that <FEM = 25°

<FEM is adjacent to <GEF, thus
$\angle GEF= \frac{360-2(25)}{2} \\ \\ = \frac{360-50}{2} = \frac{310}{2} =155^o$

<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <GEF = 155°

<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <HEG = 25°.

Row 4:

Given that <HEG = 45°

<HEG is adjacent to <GEF, thus
$\angle GEF= \frac{360-2(45)}{2} \\ \\ = \frac{360-90}{2} = \frac{270}{2} =135^o$

<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <FEM = 45°

<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <GEF = 135°.

4 0

4 years ago

Read 2 more answers

How do you write a ratio as a percent

Vikentia [17]

Take the ratio
4:8
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4/8
Divide
.5
Multiply by 100 and add a % sign
50%

3 0

4 years ago

Alberto has 92 stamps in one large álbum and 38 stamps in anotaré small álbum. How can he use mental math to find how many more

Leokris [45]

Answer:

The answer would be the large album has 54 more stamps than the small album.

Step-by-step explanation:

... 92 - 38 = 54

Do you need a drawing done though?

4 0

3 years ago

Write the equation of a polynomial of degree 3, with zeros 1, 2 and -1 where f(0)=2

drek231 [11]

Answer:

The equation of a polynomial of degree 3, with zeros 1, 2 and -1 is $x^{3}-2 x^{2}-x+2=0$

Solution:

Given, the polynomial has degree 3 and roots as 1, 2, and -1. And f(0) = 2.

We have to find the equation of the above polynomial.

We know that, general equation of 3rd degree polynomial is

$F(x)=x^{3}-(a+b+c) x^{2}+(a b+b c+a c) x-a b c=0$

where a, b, c are roots of the polynomial.

Here in our problem, a = 1, b = 2, c = -1.

Substitute the above values in f(x)

$F(x)=x^{3}-(1+2+(-1)) x^{2}+(1 \times 2+2(-1)+1(-1)) x-1 \times 2 \times(-1)=0$

$\begin{array}{l}{\rightarrow x^{3}-(3-1) x^{2}+(2-2-1) x-(-2)=0} \\ {\rightarrow x^{3}-(2) x^{2}+(-1) x-(-2)=0} \\ {\rightarrow x^{3}-2 x^{2}-x+2=0}\end{array}$

So, the equation is $x^{3}-2 x^{2}-x+2=0$

Let us put x = 0 in f(x) to check whether our answer is correct or not.

$\mathrm{F}(0) \rightarrow 0^{3}-2(0)^{2}-0+2=2$

Hence, the equation of the polynomial is $x^{3}-2 x^{2}-x+2=0$

3 0

3 years ago