If \parallelogramABCD≅\parallelogramQRST and ∡A=2x−10 and ∡Q = x+12, what is ∡A? (1 point)
Since the two parallelograms are congruent, their corresponding angles are congruent.
Therefore, ∡A = ∡Q.
In the given information, it is given that ∡Q = x+12.
Therefore, ∡A = x+12.
However, in the given information, it is also given that ∡A = 2x-10.
Therefore, x+12 = 2x-10.
Subtracting x from both sides, we get 12 = x-10.
Adding 10 to both sides, we get 12+10 = x.
Therefore, x = 22.
Substituting this value of x back into the equation ∡A = x+12, we get ∡A = 22+12 = 34.
Therefore, ∡A = 34.
Given that △QRS is congruent to △TUV, we can use the information about the corresponding sides and their lengths to solve for the value of w and find the lengths of QS and TV.
1. Given: △QRS ≅ △TUV
2. Corresponding sides:
QS ≅ TU
QR ≅ TV
RS ≅ UV
3. Given: QS = 4w + 16 and TV = 6w - 8
We can set up an equation using the given information:
4w + 16 = 6w - 8
Simplifying the equation, we will isolate w:
4w - 6w = -8 - 16
-2w = -24
Dividing both sides of the equation by -2:
w = (-24)/(-2)
w = 12
Now that we have found the value of w as 12, we can substitute it back into the given equations to find the lengths of QS and TV:
QS = 4w + 16
QS = 4(12) + 16
QS = 48 + 16
QS = 64
TV = 6w - 8
TV = 6(12) - 8
TV = 72 - 8
TV = 64
Therefore, the length of QS is 64, and the length of TV is also 64.
Wyatt is trying to prove these two triangles congruent using SAS. What is the ONE additional piece of information that he needs? (Examples for what we might need to prove congruency in a different set of triangles might include Angle B is congruent to Angle X, or segment XY is congruent to segment PT)
the image for both triangles show DEA is correspondent to GHF, there is a mark indicating a side between GH and for DE, and another for EA and HF showing that these sides are correspondent to each other
To prove congruence using the SAS (Side-Angle-Side) postulate, Wyatt would need one additional piece of information - the congruence of a corresponding side.
In this case, while Wyatt knows that angle A is congruent to angle G, and that side DE is congruent to side GH, he would need to know the congruence of another side. For example, he would need to know that side EA is congruent to side HF.
With congruent corresponding angles and two congruent corresponding sides, Wyatt could use the SAS postulate to prove the triangles congruent.
sorry, angle A is not congruent to angle G, A is correspondent to F, D is correspondent to G, and E is correspondent to H
I apologize for the misunderstanding.
To prove congruence using the SAS (Side-Angle-Side) postulate, Wyatt would need the following pieces of information:
1. Side DE is congruent to side GH (Given: DE ≅ GH)
2. Angle D is congruent to angle G (Given: ∠D ≅ ∠G)
3. Side EA is congruent to side HF (Additional information needed)
With congruent corresponding sides and angles, Wyatt can use the SAS postulate to prove the triangles congruent.