111 square units.
Find the overall rectangle's area. 8*15 = 120.
Find the missing triangle's area (which is half of a rectangle with hthe same dimensions). The dimensions (15 - 9 = 6 and 8 - 5 = 3). 6*3 = 18, divide by half to find the triangle's area. The missing triangle's area is 9 square units.
Subtract the missing triangle from the overal rectangle. 120 - 9 = 111 square units.
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the rule is: AB/n=n/BC.
from the rule above n²=AB*BC and AB=sqrt(144-n²).
After substitution n²=10*√(144-n²).
In order to solve this equation:
n⁴=100(144-n²); ⇔ n⁴+100n²-14400=0;
A general problem solving idea that's good to have in your toolbox is "the whole is equal to the sum of its parts." Here, our parts are the angles ∠STC and ∠CTU, and they combine to make the whole, angle ∠STU. We can write this as the equation
m∠CTU + m∠STC = m∠STU
Using the values m∠CTU = 89° and m∠STU = 155°, this becomes
89° + m∠STC = 155°
The only value that makes this true is 66°, so we can conclude that m∠STC = 66°.
A property of a parallelogram is that their diagonals bisect eachother. Since in part a the diagonals bisect eachother, we know for sure that it's a parallelogram.
We also know that you can make two congruent triangles with a parallelogram. Note that if you draw a line from one accute angle to the other, we create two equal triangles by SAS congruency, so since the figure is comprised of two congruent triangles, it is a parallelogram.
Given that AC ≅ BC, the sides are of equal measures.
CD is a side in both ΔACD and ΔBCD, so the side is equal in both triangles.
Given that CD if the bisector of ∠ACB, the two angles produced are equal: ∠ACD ≅ ∠BCD.
∠ACB is contained between AC and CD in ΔACD. ∠ACB is contained between BC and CD in ΔBCD.
Therefore by the SAS postulate, ΔACD ≅ ΔBCD.
The SAS postulate says that if two triangles have a contained angle between two sides that are known to be equal in the other triangle, then the triangles are congruent.
Prove that two sides are equal, then prove that an angle that is between those two sides is also equal.
i Think its C bc they are pointing out two lines so they are looking for two segments that connect with the lines.
idk if i have this right, but i believe it is "Segment Addition Postulate". the 2 sets given are congruent. and considering they are asking if the whole thing is congruent, and the 2 parts are congruent, then 2+2=4, quite literally. :P
please keep in mind that i may not be right, but it seems like the most likely answer. let me know if im wrong, please!
x = 9
E = 75 degrees
F = 91 degrees
G = 89 degrees
H = 105 degrees
Those are all of the angle measurements, but it wants the measurement of angle H. Therefore, that angle measurement is 105 degrees.