Question

Task: Find the value of x and y that proves these triangles congruent. Instructions In one part you will find the value of x that proves the triangles congruent. In the second part you will find the value ofy that proves the triangles congruent. (G.6) (2 point) Complete each of the 2 activities for this Task. Activity 1 of 2 Find the value of x.(G.6)(1 point) 24 HI 31 7x-4 to 4y+8

Answer 1

Activity 1:

We are given two triangles. The two side lengths of one triangle are known but of the other are not. Our task is to choose the value of x and y that will make the triangles congruent.

Now, the side lengths that are congruent are with 31 in the rightmost triangle and 7x -4 in the left-most triangle; therefore, equating them gives

`7x-4=31`

Similarly, side length 24 must equal 4y+8; therefore,

`4y+8=24`

Now we have to choose the values of x and y that will make both equations true.

Let us solve for x in the first equation by first adding 4 to both sides. Doing this gives

`7x=35`

Finally, dividing both sides by 7 gives

`x=5.`

Activity 2:

Now, for the value of y.

To solve for y, we first subtract 8 from both sides to get

`4y=16`

Finally, dividing both sides by 4 gives

`y=4.`

Hence, to conclude x = 5 and y = 4.