A student performed the composition rx Ro 90 on figure A. Evaluate the students completion of the composition.

Can someone help me with this please

Bingel [31]

Answer:

A.1: ∠BAC ≅ ∠BDC ≅ ∠EDF, ∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF

A.2: ∠1 ≅ ∠4, ∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6

A.3: ∠2 ≅ ∠3

B.1: ∠ACD ≅ ∠CAB, ∠CDA ≅ ∠ABC, ∠DAC ≅ ∠BCA

B.2: ∠1 ≅ ∠3 ≅ ∠5, ∠2 ≅ ∠4 ≅ ∠6

see "additional comment" regarding listing pairs

Step-by-step explanation:

There are a number of ways angles can be identified as congruent. In each case, the converse of the proposition is also true.

opposite angles of a parallelogram are congruent
corresponding angles where a transversal crosses parallel lines are congruent
alternate interior angles where a transversal crosses parallel lines are congruent
vertical angles are congruent
any two angles with the same measure are congruent

In these exercises, pairs of angles need to be examined to see which of these relations may apply.

__

ABCD is a parallelogram, so the congruent angles are opposite angles and any that are vertical or corresponding:

∠BAC ≅ ∠BDC ≅ ∠EDF ≅ 110° (3 pairs)

∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF ≅ 70° (6 pairs)

<u>Center</u>

∠1 ≅ ∠4 ≅ 66° (1 pair) . . . . vertical angles

∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6 ≅ 57° (6 pairs) . . . . marked with the same measure, and their vertical angles

<u>Right</u>

Assuming that lines appearing to go in the same direction actually do go in the same direction, the only pair of congruent angles in the figure is ...

∠2 ≅ ∠3

__

Corresponding angles in congruent triangles are congruent. Here, the congruent triangles are ΔACD ≅ ΔCAB. So, the pairs of congruent angles are ...

∠ACD ≅ ∠CAB (30°)

∠CDA ≅ ∠ABC (90°)

∠DAC ≅ ∠BCA (60°)

<u>Right</u>

The corresponding angles and any vertical angles are congruent. This means all the odd-numbered angles in the figure are congruent, and all the even-numbered angles in the figure are congruent. The marked 72° angles show the "horizontal" segments are parallel by the converse of the corresponding angles theorem.

∠1 ≅ ∠3 ≅ ∠5 (72°) (3 pairs)

∠2 ≅ ∠4 ≅ ∠6 (108°) (3 pairs)

_____

<em>Additional comment</em>

The question asks you to list pairs of congruent angles. When 3 things are congruent, they can be arranged in 3 pairs:

a ≅ b ≅ c ⇒ (a≅b), (a≅c), (b≅c)

Similarly, when 4 things are congruent, they can be arranged in 6 pairs:

a ≅ b ≅ c ≅ d ⇒ (a≅b), (a≅c), (a≅d), (b≅c), (b≅d), (c≅d)

In the above, we have elected not to list all of the pairs, but to list the set of congruences from which pairs can be chosen.

6 0

3 years ago

BRAINLIEST!! Help Solve Math Problems

NemiM [27]

9. Answer: x=4
Slope formula is y2-y1/ x2-x1. The slope will become undefined if the denominator, which is x, has a value of zero. That means the graph function would look like x=....
If the line passes point (4,3) equation of the line would be x=4

10. Answer: y=5
Slope formula is y2-y1/ x2-x1. The slope will become zero if the numerator, which is y, has a value of zero. The function would look like y=.....
The equation of the line that pass point (2,5) would be y=5

11. Answer: y=6
A line that parallel with x-axis would be a line with zero slopes and the function would be y=....
If the line passed through (1,6) the equation of the line would be y=6

12. Answer: x=-2
A line that parallel with y-axis would be a line with undefined slopes and the function would be x=....
If the line passed through (-2,4) the equation of the line would be x=-2

13. Answer: y=40
If y varies directly as x, the ratio of x:y would be kept same. It means, the ratio of y1/x1 will be equal to y2/x2. The coordinate is :
x1,y1= (5,10)
x2,y2= (20, ?)
The y when x=20 would be:
y1/x1=y2/x2
10/5= y2/20
y2= 2*20= 40

14. Answer: y=24
Same as above, if y varies directly as x, the ratio of x:y would be kept same. It means, the ratio of y1/x1 will be equal to y2/x2. The coordinate is :
x1,y1= (10,8)
x2,y2= (30, ?)
The y when x=30 would be:
y1/x1=y2/x2
8/10= y2/30
y2= 0.8*30= 24

15. Answer: x=60
If y varies directly as x, the ratio of x:y would be kept same. It means, the ratio of y1/x1 will be equal to y2/x2. Be careful because this problem is asking for x, not the y variable. The coordinate is :
x1,y1= (20,5)
x2,y2= (x2, 15)
The x2 when y=15 would be:
y1/x1=y2/x2
5/20= 15/x2
x2= 15 /0.25 = 60

3 0

4 years ago

What is the probability that a whole number between 1 and 12, selected at

olga2289 [7]

First, find multiples of 2 and 3 in 1-12
2,3,4,6,8,9,10,12
8 out of 12 are a multiple of 2 or 3
8/12
reduce
2/3 is the probability

Hope i help! plz give brainliest if possible

7 0

3 years ago

the ratio of boys to girls are 8 to 7. if there was a total of 195 students, how many boys and girls are there?

Misha Larkins [42]

Add the values of the ratio.

8+7= 15

Boys: 195/15= 13(8)=104

Girls: 195/15= 13(7)= 91

There are 104 boys and 91 girls. Hope this helps!

8 0

3 years ago

Sociologists have found that information spreads among a population at an exponential rate. How do you think this happens? Descr

liq [111]

Answer: Because people talk about important information

Step-by-step explanation: like a virus, information spreads like wildfire. But good news that has spread around my community is that we have a bunch of motivated people looking forward to feeding the homeless and create a homeless shelter to get back on their feet. Thanks to flyers, friends, and family enough money was raised to successfully build a homeless shelter.

3 0

3 years ago