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ddd [48]
2 years ago
14

Sketch and prove the following for the two congruent triangles ∆ABC and ∆DEF.

Mathematics
1 answer:
madreJ [45]2 years ago
3 0

Answer:

See explanation

Step-by-step explanation:

<u>Given:</u> ΔABC ≅ ΔDEF

AM, DN - medians

<u>Prove:</u> AM ≅ DN

Proof:

1. Congruent triangles ABC and DEF have congruent corresponding parts:

  • AB ≅ DE;
  • BC ≅ EF;
  • ∠ABC ≅ ∠DEF.

2. BM ≅ MC - definition of the median AM;

3. EN ≅ NF - definition of the median DN;

4. AB ≅ 2BM, EF ≅ 2EN

BM ≅ 1/2 AB,

EN ≅ 1/2 EF,

thus, BM ≅ EN

5. Consider two triangles ABM and DEN. In these triangles \:

  • AB ≅ DE (see 1));
  • BM ≅ EN (see 4));
  • ∠ABM ≅ ∠DEN (see 1).

So, ΔABM ≅ ΔDEN by SAS postulate.

6. Congruent triangles ABM and DEN have congruent corresponding sides BM and DN.

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Zoe jogs 3/4 of a mile every 1/5 of an hour.
stepan [7]

Answer:

15/4 please let me know if this helped you :)

Step-by-step explanation:

0.75*5=3.75 or 15/4

all of your answers are less than 3/4ths of a mile...she is increasing the amount she runs not decreasing.

3 0
2 years ago
A) what is the slope of the parallel to y=2x+3
tekilochka [14]

Answer:

a) 2 b) -1/2

Step-by-step explanation:

a) im pretty sure the question only asks for the slope of the parallel line y=2x+3, that that would be 2 because they have the same slope

b) the question is phrased weird, but im assuming it wants the same thing from a, (the slope) and the slope of a perpendicular like is always the opposite reciprocal of the original number

for example in y=2x+3:

2 is the original slope

meaning that the perpendicular would be -1/2

<em>the</em><em> </em><em>images</em><em> </em><em>above</em><em> </em><em>are</em><em> </em><em>just</em><em> </em><em>examples</em><em> </em><em>and</em><em> </em><em>are</em><em> </em><em>not</em><em> </em><em>related</em><em> </em><em>to</em><em> </em><em>the</em><em> </em><em>answer</em>

6 0
3 years ago
What is g(x-5) when g(x)=-2x+4?
Oksi-84 [34.3K]
G(-2x + 4 - 5)g(-2x -1)
I think this is how you start it?? not sure
4 0
3 years ago
Read 2 more answers
The minimum point on the graph of the equation y = f(x) is (-1, -3). What is the minimum point
vladimir1956 [14]

Answer:

(4, -3)

Step-by-step explanation:

the equation f(x-5) is a translation of the equation f(x) by 5 units to the right.

So, if all points of the equation f(x) are shifted 5 units to the right, the minimum point of the graph is also shifted 5 units to the right, so to find the minimum point of y = f(x - 5), we just need to sum 5 units to the x-coordinate:

Minimum point = (-1 + 5, -3) = (4, -3)

So the minimum point of y = f(x - 5) is (4, -3).

7 0
3 years ago
A regular decagon is rotated n degrees about its center, carrying the decagon onto itself. The value of n could be:
Delicious77 [7]

Answer:

252°

Step-by-step explanation:

Given

Shape: Decagon

Required

Determine the value of n

A Decagon has 10 sides and a complete rotation takes 360°

First, we need to calculate the angle of each rotation as follows.

Each Rotation = ⅒ * 360°

Each Rotation = 360°

Next, we determine the possible values of n.

The statement is represented as "possible values of n" because n can assume infinite number of values.

However, n must be a multiple of 36

From the list of given options.

10, 150 and 225 are not multiples of 36

Only 252 happens to be a multiple of 36 from the list of given options.

Hence, option D answers the question [base on the given options]

4 0
2 years ago
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