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3 years ago

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Identify the property that justifies the statement. ∠XYZ≅∠PDQ and ∠PDQ≅∠ABC, so ∠XYZ≅∠ABC.

1 answer:

MArishka [77]3 years ago

3 0

Answer: Transitive property of Equality.

Therefore if ∠XYZ≅∠PDQ and ∠PDQ≅∠ABC then by transitive property of equality we have ∠XYZ≅∠ABC.

The law of transitivity tells that if a equals to b and b equals to c then a equals to c.

For example If Jane has same height of Susan and Susan has same height of Tina then Jane has same height of Tina.

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Solve the triangle given that a=19 b=16, c=11.

kirill [66]

Answer:

The angles of the triangle are approximately 87.395º, 57.271º and 35.334º.

Step-by-step explanation:

From statement we know all sides of the triangle ( $a$ , $b$ , $c$ ), but all angles are unknown ( $A$ , $B$ , $C$ ). (Please notice that angles with upper case letters represent the angle opposite to the side with the same letter but in lower case) From Geometry it is given that sum of internal angles of triangles equal 180º, we can obtain the missing information by using Law of Cosine twice and this property mentioned above.

If we know that $a = 19$ , $b = 16$ and $c = 11$ , then the missing angles are, respectively:

Angle A

$a^{2} = b^{2}+c^{2}-2\cdot b\cdot c \cdot \cos A$ (1)

$A = \cos^{-1}\left(\frac{b^{2}+c^{2}-a^{2}}{2\cdot b\cdot c} \right)$

$A = \cos^{-1}\left[\frac{16^{2}+11^{2}-19^{2}}{2\cdot (16)\cdot (11)} \right]$

$A \approx 87.395^{\circ}$

Angle B

$b^{2} = a^{2}+c^{2}-2\cdot a\cdot c \cdot \cos B$ (2)

$B = \cos^{-1}\left(\frac{a^{2}+c^{2}-b^{2}}{2\cdot a\cdot c} \right)$

$B = \cos^{-1}\left[\frac{19^{2}+11^{2}-16^{2}}{2\cdot (19)\cdot (11)} \right]$

$B\approx 57.271^{\circ}$

Angle C

$C = 180^{\circ}-A-B$

$C = 180^{\circ}-87.395^{\circ}-57.271^{\circ}$

$C = 35.334^{\circ}$

The angles of the triangle are approximately 87.395º, 57.271º and 35.334º.

8 0

3 years ago

Look at the figure what is the value of y √2y+3=11

Natasha_Volkova [10]

Answer:

y=2

Step-by-step explanation:

first solve those in the brackets then find the square root

2y+3=11

put like terms together

3 goes to the right side

2y=11-3

2=8

y=4

√4=2

y=2

3 0

4 years ago

Write a rule for a function with a parabolic graph that contains the x-intercepts (-20,0) and (40,0) and a maximum point whose y

lakkis [162]

Step-by-step explanation:

Since the x-intercepts are -20 and 40, the line of symmetry is x = (-20 + 40)/2 = 10.

Now we have y = a(x - 10)² + 30, where a is an unknown constant. We can find a by using an x-intercept point.

=> (0) = a[(40) - 10]² + 30

=> 900a + 30 = 0, a = -1/30.

Hence the rule is y = -(x - 10)²/30 + 30.

7 0

3 years ago

Quadrilateral A B C D is shown. All sides are congruent. Angle C is a right angle.

MAXImum [283]

Answer:

The first one and last one

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Without finding the inverse of the function, determine the range of the inverse of f left parenthesis x right parenthesis equals

natta225 [31]

c

The domain of the function is all real numbers greater than or equal to 0.

The range of the function is all real numbers greater than or equal to −1.

The range of the function is all real numbers less than or equal to 0.

The domain of the function is all real numbers less than or equal to 0

7 0

2 years ago