Step-by-step explanation:
YO ≅ NZ
Given
YO + OZ ≅ NZ + OZ
Additive property
YZ ≅ NO
Segment addition postulate
∠M ≅ ∠X, ∠N ≅ ∠Y
Given
ΔMNO ≅ ΔXYZ
AAS congruence
Answer:
a = 6
Step-by-step explanation:
Area = 36 
Only one number will make this missing length true.
Obviously it's a square so one number x one number will equal to 36 
6 x 6 = 36 
For the first one, you did good. I will just suggest a couple things.
Statement Reason
JK ≅ LM Given
<JKM ≅ < LMK Given (You did both of these steps so well done.)
MK ≅ MK Reflexive Property (Your angle pair is congruent but isn't one of the interior angle of the triangles you are trying to prove.)
ΔJMK ≅ ΔLKM SAS
Problem 2: (You also have a lot of great stuff here.)
Statement Reason
DE ║ FG Given
DE ≅ FG Given
<DEF≅<FGH Given
<EDF≅<GFH Corresponding Angles (You don't need to know that F is the midpoint but you got corresponding angle pair which is correct.)
ΔEDF≅ΔGFH ASA
<DFE≅<FHG CPCTC
The drawing shows a circle, with the two lines forming a cross assumed to be perpendicular to each other, so this is most likely to be a square, as the four points at which the perpendicular lines intersect with the circle can be connected to form a square.
We would need 3 points for an equilateral triangle, 5 for a pentagon, and 6 for a hexagon, which do not fit the current steps.
Given:
- Lily bought 20.24 pounds of grapefruit.
- The lightest grapefruit weighed 1.2 pounds.
- The heaviest grapefruit weighed 1.8 pounds.
To Find:
An estimate of the number of grapefruits she bought.
Answer:
The best estimate is that Lily bought 13 grapefruits.
Step-by-step explanation:
Given that the lightest grapefruit weighed 1.2 pounds and the heaviest one weighed 1.8 pounds, we can take the mean or average of these two weights to estimate the weight of any of the grapefruits that she bought.
That is, we can say that each grapefruit must weigh something close to the average value.
The average can be found as

Thus, the average grapefruit from the bundle she bought must weigh around 1.5 pounds.
Now, given that the total weight of the grapefruit she bought is 20.24 pounds.
By the Unitary Method,
Weight of One Grapefruit = Total Weight of All Grapefruits ÷ Number of Grapefruits
So, number of grapefruits she bought = Total weight ÷ weight of one grapefruit
In other words,
number of grapefruit = 
Rounding off, we may say that Lily bought 13 grapefruits.