Triangles ΔABC ≅ ΔBAD so that C and D lie in the opposite semi-planes of segment AB. Prove that segment CD bisects segment AD.
1 answer:
Answer:
See explanation
Step-by-step explanation:
Triangles ΔABC and ΔBAD are congruent. So,
- AB ≅ BA;
- AC ≅ BD;
- BC ≅ AD;
- ∠ABC ≅ ∠BAD;
- ∠BCA ≅ ∠ADB;
- ∠CAB ≅ ∠DBA.
Consider triangles AEC and BED. In these triangles,
- AC ≅ BD;
- ∠EAC ≅ ∠EBD (because ∠CBA ≅ ∠BAD);
- ∠AEC ≅ ∠BED (as vertical angles).
So, ΔAEC ≅ ΔBED. Thus,
AE ≅ EB.
This means that segment CD bisects segment AD.
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Answer:
The answer is below
Step-by-step explanation:
From the image of the leaning tower of Pisa, we can see that it passes through the point (7.75, 0) and (10.75, 42).
a) The equation of a line in slope intercept form is given by y = mx + b, where m is the slope and b is the intercept. Also, the equation of line passing through
Hence since it passes through (7.75, 0) and (10.75, 42), the equation is:
b) When the tower is 56 meters tall, i.e. y = 56, we need to find the value of x:
y = 14x - 108.5
56 = 14x - 108.5
56 + 108.5 = 14x
164.5=14x
x = 164.5/14
x = 11.75
When the tower is 56 meters tall, the top of the tower is 11.75 m off center