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:
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B) 71.56°
C) 36.88°
Step-by-step explanation:
To solve each part of the problem, let's pay attention to the triangle ABC shown in the figure.
A) The slant height (l) of the cone is the hypotenuse of the right triangle ABC, then, to calculate it you can apply the Pythagorean Theorem:
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∠°
C) The angle formed between the segments (which you can call α) that represent the slant heights is twice the angle ∠C.
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∠
Then:
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