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2 years ago

To prove that δdef ≅ δdgf by sas, what additional information is needed? ∠def ≅ ∠ dgf ∠dfe ≅ ∠ dfg de ≅ dg dg ≅ gf.

Mathematics

1 answer:

snow_lady [41]2 years ago

5 0

Reflection:

Reflection is a type of rigid transformation which requires the turning of an object, shape or figure about a reference point or line. Therefore, the needed additional information is ∠DFE ≅ ∠ DFG.

Reflection implies turning the given triangle DEF about its side DF, so as to produce an image with the same dimensions but different orientation.

The required proof by Side-Angle-Side (SAS) implies that the relations will be in respect of two of its sides and their included angle.

So According to the above statement,

GF ≅ FE (: given)

DF is the common side to triangles DEF and DFG.

DFG is the included side.

Thus ∠DFE ≅ ∠ DFG (Side-Angle-Side postulate, SAS)

Learn more about Reflection on:

brainly.com/question/26494295

#SPJ4

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How do i find the slope

Elodia [21]

Hi, I'm happy to help!

To find the slope, you need to use the slope formula, where m is the slope:

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

Slope means rise over run, or how much the line rises per the amount the line moves forward. This equation shows the movement from the y points to show rise, over the difference in the x points to show run.

Now, to find the slope we insert our values, starting with our second y point:

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

Now insert our first y point:

m= $\frac{2-4 }{x_{2} -x_{1} }$

Now we insert our second x point:

m= $\frac{2-4 }{-3 -x_{1} }$

And finally our first x point:

m= $\frac{2-4 }{-3 -3 }$

Now, we solve:

m= $\frac{-2 }{-6}$

So, our slope is -2/-6, to simplify it, we remove both negatives because they cancel each other out.

m= $\frac{2 }{6}$

Now, we simplify our fraction by dividing the top and bottom by 2:

m= $\frac{1}{3}$

So, our slope is 1/3. This means that for every 1 unit the line rises, it goes to the right 3 units. The y-intercept is where the line hits the y axis.

If the question is asking for slope intercept form for the equation, you use y=mx+b

y represents any y coordinate on your line, m represents your slope (1/3), x represents any x coordinate on your line, and b represents your y-intercept (3).

If you were to insert these values, you would get:

y= $\frac{1}{3}$ x+3

You use this to find what a y coordinate would be so you can draw your line.

For the next equation we do the same thing:

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

Insert our values:

m= $\frac{4-1}{2-(-4)}$

Get rid of the double negative:

m= $\frac{4-1}{2+4}$

Solve:

m= $\frac{3}{6}$

Simplify:

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

Now that we know our slope, let's plug it in to our slope intercept form equation.

y= $\frac{1}{2}$ x+3

I hope this was helpful! Keep learning! :D

5 0

3 years ago

What is the lateral surface area of the square pyramid below?

den301095 [7]

Answer:

lateral surface area = 48 inches²

Step-by-step explanation:

The picture below is the square base pyramid you are referring. The lateral area is adding the area of the 4 triangles in the pyramid.

area of a triangle = 1/2 × b × h

The slant height of the triangle is gotten using Pythagoras theorem

lateral surface area = 4 × (1/2 × 3 × 8)

lateral surface area = 4 × 24/2

lateral surface area = 4 × 12

lateral surface area = 48 inches²

3 0

3 years ago

Read 2 more answers

EXTRA POINTS PLEASE HELP I'LL GIVE BRAINLIEST Please write a 2 column proof :)

lidiya [134]

Answer:

Step-by-step explanation:

1). segment AB ≅ segment AE ......... 1). Given

2). ΔBAE is isosceles .............. 2). Definition of isosceles Δs

3). ∠ABC ≅ ∠AEB ............. 3). Corollary to isosceles Δs theorem

4). segment BG ≅ segment EF ........ 4). Definition of midpoints

5). segment BC ≅ segment ED ......... 5) Given

6). segment CD ≅ segment DC ....... 6). Reflexive property

7). segment BD ≅ segment EC ........ 7). Property of sum of equals parts

8). ΔBGD ≅ Δ EFC ............... 8). SAS postulate

9). ∠1 ≅ ∠2 ............ 9). Corresponding parts of congruent Δs

10). ΔCHD is isosceles ............ 10). Corollary to isosceles Δs theorem

7 0

3 years ago

The angle bisectors of AXYZ are XG, YG, and ZG. They meet at a single point G.

Harrizon [31]

Answer:

m∠FXD = 36°

EG = 10

m∠FZG = 24°

Step-by-step explanation:

In triangle XYZ, G is the incenter of the triangle.

Since, m∠FXG = 18°

And m∠FXD = 2(m∠FXG)

= 2 × 18°

= 36°

Since, point G is equidistant from all sides (Property of incenter of a triangle)

Therefore, DG = EG = GF = 10

Since, m∠X + m∠Y + m∠Z = 180°

2(m∠FXG) + m∠DYE + 2(m∠FZG) = 180°

2(18)° + 96° + 2(m∠FZG) = 180°

2(m∠FZG) = 180° - 132°

m∠FZG = 24°

3 0

3 years ago

Helphelphelphelphelp

USPshnik [31]

Answer:

you would've spent $10.50.

you saved $25.50.

you saved 70%.

Step-by-step explanation:

since its 7/10, 10 indicates that it'll be out of 100. so its 70% off of 35.

7 0

3 years ago