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3 years ago

Part 3: Choose a proof method.

1 answer:

3 0

The given congruences are corresponding sides and angles of ΔWZX and ΔYZX. Segment ZX is congruent to itself, so ΔWZX ≅ ΔYZX by SAS.

Then ∠WXZ ≅ ∠YXZ and WX ≅ YX by CPCTC. The latter means X is a midpoint and that ZX is a bisector of WY. The former means the angles of the linear pair ∠WXZ and ∠YXZ must both be 90°, as they are both congruent and supplementary.

Therefore, ZX is perpendicular to WY and also its bisector.

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Question:

aivan3 [116]

Answer:

part A) The scale factor of the sides (small to large) is 1/2

part B) Te ratio of the areas (small to large) is 1/4

part C) see the explanation

Step-by-step explanation:

Part A) Determine the scale factor of the sides (small to large).

we know that

The dilation is a non rigid transformation that produce similar figures

If two figures are similar, then the ratio of its corresponding sides is proportional

Let

z ----> the scale factor

$\frac{CB}{C'B'}=\frac{CD}{C'D'}=\frac{BD}{B'D'}$

The scale factor is equal to

$z=\frac{CB}{C'B'}$

substitute

$z=\frac{4}{8}$

simplify

$z=\frac{1}{2}$

Part B) What is the ratio of the areas (small to large)?

Area of the small triangle

$A=\frac{1}{2}(2)(4)=4\ units^2$

Area of the large triangle

$A=\frac{1}{2}(4)(8)=16\ units^2$

ratio of the areas (small to large)

$ratio=\frac{4}{16}=\frac{1}{4}$

Part C) Write a generalization about the ratio of the sides and the ratio of the areas of similar figures

In similar figures the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In similar figures the ratio of its areas is equal to the scale factor squared

4 0

4 years ago

Which expression has a value of 23?

DaniilM [7]

A) $7 - (-16) = \fbox {23}$

B) $-3 - 20 = \fbox {-23}$

C) $10 - 13 = \fbox {-3}$

D) $-18 - (-5) = \fbox {-13}$

You were correct, the exact answer is A. The others do not equal 23 besides that one. Good job!

6 0

3 years ago

Read 2 more answers

Find the least common multiple of these two expressions 8v^5w^8 and 14

Morgarella [4.7K]

True..............................................

4 0

4 years ago

54.00 for tickets write a unit rate for the situation

schepotkina [342]

54 dollars/1 ticket.
sorry couldnt find fraction bar used / instead .

6 0

3 years ago

Janice works for a salary of $2,396 per month. She has federal income tax withheld at the rate of 15 percent, Social Security ta

MAVERICK [17]

Given that Janice monthly salary is $2,396. And she has deductions of federal income tax withheld at the rate 15%, social security tax at the rate of 6.2% and medicare tax at the rate of 1.45% and health insurance premium worth 95$ per month.

Let us calculate total deductions.

Federal income tax = 15% of 2396 = 0.15*2396 =$359.4

Social security tax = 6.2% of 2396=0.062*2396 =$148.552

Medicare tax = 1.45% of 2396= 0.0145*2396=$34.742

health insurance premium =$95

Total deductions = $637.694

To calculate Janice net pay we have to subtract deductions from monthly salary that is 2396-637.694 = $1758.306

Hence net pay of Janice is $1758.306 per month.

4 0

3 years ago