All categories

3 years ago

Are triangles the congruent? Write the congruency statement.

Mathematics

1 answer:

Ede4ka [16]3 years ago

4 0

Answer:

Yes. but under the next condition m∠Q ≅ m∠T

Step-by-step explanation:

If the circular arc label of the angles ∠Q and ∠T means that they are congruent (equal) or m∠Q ≅ m∠T, in that case we can prove that ΔPQR is congruent with ΔSTU or ΔPQR≅ΔSTU.

We need three elements to form congruency statement.

1. Sides PQ ≅ ST = 4 ft

2. Angles m∠Q ≅ m∠T

2. Sides QR ≅ TU = 6 ft

Based on the SAS statement ( Side-Angle-Side) we prove that:

ΔPQR ≅ ΔSTU.

If they are congruent, every corresponding elements are congruent:

Sides PR = SU => 3y - 2 = y + 4 => 3y - y = 4 + 2 => 2y = 6 => y = 6/2 = 3

y = 3 => PR = 3 · 3 - 2 = 9 - 2 = 7 => PR = 7 ft

Perimeter of ΔPQR is

P = PQ + QR + PR = 4 + 6 + 7 = 17 ft

P = 17 ft

God with you!!!

You might be interested in

Evaluate 2r²+3s³-r²+4+²-r²

Vilka [71]

$2r^2 + 3s^3-r^2+4^2+-r^2 \\ \\ 2r^2 + 3s^3 - r^2 + 16 + -r^2 \\ \\ 2r^2 + 3s^3 = r^2 16 - r^2 \\ \\ (2r^2 - r^2-r^2) + 3s^3+ 16 \\ \\ 3s^3 + 16 \\ \\ Answer: 3s^3 + 16$

7 0

3 years ago

Read 2 more answers

Given the following data set 2,3,1,6,1,1,1,0,2,4,5,1,2,2,3 Mean Median Range Mid range

igomit [66]

Answer:

mean: 34/15=2.27

median: 2

range: highest-lowest...... 6-0=6

mid range: high + low divided by 2

6+0=6/2=3

8 0

3 years ago

Read 2 more answers

Why does the associative property work with addition but not subtraction?

lbvjy [14]

Answer:

Contrary to addition, subtraction doesn't have the associative property. If we subtract the first two numbers, 10 minus 5, it gives us 5. ... Changing the way of associating the numbers in subtraction changes the answer. Thus, subtraction doesn't have the associative property.

Step-by-step explanation:

8 0

3 years ago

Find the equation of the line with a slope of − 1/2 through (4, 5)

STALIN [3.7K]

Answer: Hello:

Slope - intercept form is y = mx + b.

Since -1/2 is your slope and 5 is your y - intercept, all you need to do is substitute those values into the equation:

y = -1/2 + 5

Hope this helps!

5 0

3 years ago

A line passes through (2,-1) and (4,5). What answer is the equation of the line? -3x+5y=-13

Sliva [168]

The equation of the line passes through (2, -1) and (4, 5) is -3x + y = - 7 So, option 2 is correct.

Solution:

Given, two points are (2, -1) and (4, 5)

We have to find that a line that passes through the given two points.

First let us find the slope of the line that passes through given two points.

So, slope of line "m" is given as:

$\mathrm{m}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text { where, }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right) \text { are two points on line. }$

So slope of our line = $\frac{5-(-1)}{4-2}=\frac{5+1}{2}=3$

Now, let us find the line equation using point slope form:

$y-y_{1}=m\left(x-x_{1}\right) \text { where } m \text { is slope and }\left(x_{1}, y_{1}\right) \text { is point on the line. }$

Then equation of line is,

y – 5 = 3(x – 4)

y – 5 = 3x – 12

-3x + y = 5 – 12

-3x + y = -7

Hence, the line equation is -3x + y = - 7 so, option 2 is correct.

4 0

3 years ago