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WARRIOR [948]
3 years ago
7

ABC is an isosceles triangle with BA=BC

Mathematics
1 answer:
melomori [17]3 years ago
5 0

Explanation:

1. ∠BAC≅∠BCA, ∠ABD≅∠ADB; Reason: definition of isosceles triangles

2. ∠ABD +∠BAC +∠ADB = 180°; Reason: sum of internal angles is 180°

3. ∠BAC = 180° -2(∠ABD) = 36°; Reason: Subtraction and substitution properties of equality

4. ∠BAC +∠BCA +∠ABC = 180°; Reason: sum of internal angles is 180°

5. ∠BCA = 180° -2(∠BAC) = 108°; Reason: Subtraction and substitution properties of equality

6. ∠ABD +∠DBC = ∠ABC; Reason: Angle sum theorem

7. ∠DBC = ∠ABC -∠ABD = 108° -72° = 36°; Reason: Subtraction and substitution properties of equality

8. ∠BCA = ∠BAC = 36°; Reason: Substitution property of congruence

9. ΔBCD is isosceles; Reason: Base angles DBC and BCA are congruent.

_____

There may be extra steps involved if you separately use subtraction and substitution properties of equality, or if you separately claim congruence of angles and equality of their measures. We have assumed that the definition of "isosceles triangle" includes the fact of equal side lengths <u>and</u> equal base angles.

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Next, choose a value to the far left, between each of the zeroes, and to the far right to evaluate if it makes a true statement when input into the given inequality.

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3 0
1 year ago
Both 2 and 5 are common factors of a number. The number in between 101 and 118. What is the number? Give a reason for your answe
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Your answer must be a multiple of 10 and there is only one answer in that range that fits. 

Double-check: 
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1.
antoniya [11.8K]

Answer:

B

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