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Shtirlitz [24]
3 years ago
14

20 points!! Please help!!!

Mathematics
1 answer:
kolezko [41]3 years ago
4 0

Answer:

The third option is the correct one.

Step-by-step explanation:

For similar triangles, the angles are the same, but the distances between corresponding vertices is only proportional

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in the given figure ,o is the centr of the circle, ab is the diameter and do is perpendicular to ab. prove that angle AEC= ANGLE
maksim [4K]

The given triangles ΔDOA and ΔABC are right triangles that have a

common vertex at point <em>A</em>.

  • <u>ΔDOA is similar to ΔABC, and </u><u>∠AEC</u><u> is equal to </u><u>∠ABC,</u><u> therefore, ∠AEC = ∠ODA</u>

Reasons:

The given parameters are;

The diameter of the circle with center <em>O</em> = AB

DO ⊥ AB (DO is perpendicular to AB)

Required:

Prove that ∠AEC = ∠ODA

A two column proof is presented as follows;

Statement {}                                                 Reason

1. AB is the diameter of circle     <em> </em>{}                 1. Given

2. DO is perpendicular to AB <em> </em>{}                     2. Given

3. ∠DOA = 90° <em> </em>{}                                             3. Definition of DO ⊥ AB

4. ∠BCA = 90°  <em> </em>{}                                             4. Thales theorem

5. ∠BCA ≅ ∠BCA <em> </em>{}                                         5. Reflexive property

6. ΔDOA ~ ΔABC  <em> </em>{}                                        6. AA similarity postulate

7. ∠ABC ≅ ∠ODA  <em> </em>{}                                       7. CASTC

8. ∠ABC = ∠ODA  <em> </em>{}                                        8. Definition of congruency

9. ∠AEC ≅ ∠ABC  <em> </em>{}                                        9. Angles in the same segment

10. ∠AEC = ∠ABC  <em> </em>{}                                       10. Definition of congruency

11. ∠AEC = ∠ODA  <em> </em>{}                                        11. Transitive property of equality

In statement 6, ΔDOA is similar to ΔABC by Angle-Angle, AA, similarity

postulate, therefore, the three angles of ΔDOA are congruent to the three

angles of ΔABC.

Therefore ∠ABC ≅ ∠ODA by Corresponding Angles of Similar Triangles

are Congruent, CASTC.

Learn more about circle theorem here:

brainly.com/question/16879446

7 0
2 years ago
Remember that you may need to regroup to subtract. 651,784 - 482,638=
Mazyrski [523]

Answer:

169146

Step-by-step explanation:

7 0
3 years ago
A rectangular-prism-shaped toy box is 2 cm by 1 cm by 1 cm. a storage bin is packed with 18 of these toy boxes. there is no extr
Virty [35]
The bin's volume is 36cm³
6 0
3 years ago
What are the zeros of the function f(x) = x2 + 5x + 5 written in simplest radical form?
Pavel [41]

\boxed{x_{1}=\frac{-5 + \sqrt{5}}{2}} \\ \\ \\ \boxed{x_{2}=\frac{-5 - \sqrt{5}}{2}}

<h2>Explanation:</h2>

Using the quadratic formula:

x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ \\ Here: \\ \\ f(x) = x^2 + 5x + 5 \\ \\ \\ So: \\ \\ a=1 \\ \\ b=5 \\ \\ c=5 \\ \\ \\ x=\frac{-5 \pm \sqrt{5^2-4(1)(5)}}{2(1)} \\ \\ x=\frac{-5 \pm \sqrt{25-20}}{2} \\ \\ x=\frac{-5 \pm \sqrt{5}}{2} \\ \\ \\ Two \ solutions: \\ \\ \boxed{x_{1}=\frac{-5 + \sqrt{5}}{2}} \\ \\ \\ \boxed{x_{2}=\frac{-5 - \sqrt{5}}{2}}

<h2>Learn more:</h2>

Quadratic functions: brainly.com/question/12164750

#LearnWithBrainly

8 0
2 years ago
Maggie has $40 to buy a new dress and hair accessory for her school dance the dress she wants cost $35.75 the cost of her hair a
jonny [76]

Answer:

Yes Maggie has enough money to purchase the dress and hair accessory.

Step-by-step explanation:

Dress = $35.75

Hair accessory = $2.80

Total amount of money = $40

Does her have enough money?

Total Money in pocket - (Dress cost + hair accessory)

 $40.00 - ($35.75 + 2.80)

  $40.00 - ($36.00 + $3.00)     Round to the nearest dollar

  $40.00 - $39.00 = $1.00

Yes

8 0
2 years ago
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