There are several conditions where triangles can be proved similar:
AA - where two of the angles are same.
SAS - where two sides of a triangle compare to the corresponding sides in the other are in same proportion, and the angle in the middle are equal.
SSS - Where all sides in a triangle and the corresponding sides are in the same proportion.
In the case above, we can only use the method of SAS, as only two sides of the triangles are given.
<HMG = <JMK (vertically opposite angles)
HM/MK = 8/12 = 2/3
GM/MJ = 6/9 = 2/3
As the two sides of a triangle comparing to the corresponding sides in the other are in same proportion, and the angle in the middle are equal, the above triangles are similar, with the prove of SAS.
Therefore, the answer is C.yes by SAS.
Hope it helps!
Answer:
k = -9.
Step-by-step explanation:
As the triangle is right-angled at Q, by Pythagoras:
PR^2 = PQ^2 + RQ^2
So, substituting the given data and using the distance formula between 2 points:
(7 - 1)^2 + (k - 4)^2 = (-4-4)^2 + (-3-1)^2 + (7 - (-3))^2 + (k - (-4))^2
36 + (k - 4)^2 = 64 + 16 + 100 + ( k + 4)^2
(k - 4)^2 - (k + 4)^2 = 180 - 36
k^2 - 8k + 16 - (k^2 + 8k + 16) = 144
-16k = 144
k = -9.
Answer:
Yes, it will fit snugly in a 90º corner
Step-by-step explanation:
To do this, we simply need to check if the given sides of the shelf is right-angled.
So, we have:
To check for right-angle triangle, we make use of:
This gives:
This shows that the given sides of the shelf is a right-angled triangle.
Hence, it will fit the wall
