Answer:
ASA and AAS
Step-by-step explanation:
We do not know if these are right triangles; therefore we cannot use HL to prove congruence.
We do not have 2 or 3 sides marked congruent; therefore we cannot use SSS or SAS to prove congruence.
We are given that EF is parallel to HJ. This makes EJ a transversal. This also means that ∠HJG and ∠GEF are alternate interior angles and are therefore congruent. We also know that ∠EGF and ∠HGJ are vertical angles and are congruent. This gives us two angles and a non-included side, which is the AAS congruence theorem.
Since EF and HJ are parallel and EJ is a transversal, ∠JHG and ∠EFG are alternate interior angles and are congruent. Again we have that ∠EGF and ∠HGJ are vertical angles and are congruent; this gives us two angles and an included side, which is the ASA congruence theorem.
Answer:
Step-by-step explanation:
<h3>
The complete exercise is: "A rectangular yard is 20 ft by 15 ft. The yard is cover with grass except for 8.5 feet square flower garden. How much grass is in the yard?"</h3><h3 />
The area of a rectangle can be calculated with the following formula:
Where "l" is the lenght of the rectangle and "w" is the width.
Based on the data given in the exercise, you can identify tha the length and the width of the rectangular yard are:
Then, you can substitute these values into the formula and then evaluate in order to find the area of the entire yard:
The area of the flower garden which is an square, can be calculated with this formula:
Where "s" is the side length.
In this case you know that:
Then the area of the flower garden is:
<em> </em>Since this is not covered with grass, you need to subtract both areas calculated above in order to find the surface covered with grass in the yard.
This is: