Prove Proposition 55: Angle Bisector Theorem The set of points on a proper angle or in its interior that are equidistant from the sides of the angle is the angle bisector.

Q: Let a, b, and c be the sides of a triangle and let 0 be the angle opposite c. Use the Law of Cosines…

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Q: every exterior angle is supplementary to its adjacent interior angle true or false

A: We will check if the statement is true.

Q: Find all angles that are coterminal with the given angle. (Let k be an arbitrary integer.) −15°

A: Given angle-15°we have to find all angles that are coterminal with the given angle-15°Let , A=-15°

Q: Find a positive angle less than 360° or 2π that is coterminal with the given angle 23π/5.

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Q: Which statement(s) are true about inscribed angles? Statement 1: The vertex of an inscribed angle…

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Q: Which of the following is/are Euclid's axiom/s? I. All right angles are equal. II. One can describe…

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Q: True or False: The triangles shown in the figure below are congruent by the SAS Postulate

A: True. The triangles shown in the figure below are congruent by the SAS Postulate.

Q: Prove that triangle AOT is congruent to triangle ABE by completing the two-column proof. A 0 Given:…

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Q: Indicate whether the statement is true or false. According to the Angle-Addition Postulate, m∠ABD +…

A: Given,          An angle is shown below :

Q: 3. Which of the following statements is true about an angle drawn in standard position? O Positive…

A: Explain the each options and than choose the correct.

Q: Prove the Angle-Angle-Side Theorem in Neutral Geometry: If △ABC and △DEF are triangles so that ∠ACB…

A: Given: In the triangle ∆ABC  & ∆DEF ∠ACB ≅ ∠DFE∠BAC ≅ ∠EDF       AB ≅ DE   To prove: ∆ABC ≅ ∆DEF…

Q: 13. The sides of an inscribed angle are two chords that intersect at a point on the circle. 14 Fach…

A: NOTE: As per our guidelines, I have stated thirteenth problem in the picture. If you want the…

Q: Let a, b, and c be the sides of a triangle and let θ be the angle opposite c. Use the Law of Cosines…

A: Given  a, b, and c the sides of a triangle and θ the angle opposite to the side c. To prove the…

Q: find all angles that are coterminal with the given angle. (let k be an arbitrary integer) -225…

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Q: Prove that 30° is a constructible angle.

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Q: 6. Let AABC be a triangle and let D be a point on the side BC. Let 0, be the center of the inscribed…

A: Given data-   we have given a triangle ABC .  O1 = The center of the inscribed circle in triangle…

Q: Find a positive angle less than 360° that is coterminal with the given angle. 540° A positive angle…

A: We can find the coterminal angles of a given angle by using the following formula: Coterminal angles…

Q: a Parallel Lines in Proofs 3. Given: DE || BC B is the midpoint of AD DE BC Prove: 4C LE °.…

A: Congruent triangles

Q: Prove Proposition 59: Isosceles Triangle Theorem A. A triangle is isosceles iff it has a pair of…

A: Given Prove that the triangle is an isosceles triangle if (A) the triangle has pair of congruent…

Q: Prove that if two angles are complementary, then both are acute

A: We can prove the statement as below.

Q: . Prove Theorem 5-11 on page 178: The segment that joins the midpoints of two sides of a triangle is…

A: Let M and N be the midpoints of the sides AB and AC respectively. To prove: MN||BC and MN=12BC

Q: Given: AB = AC, BD = CD Prove: AD bisects ZCAB

A: Solved below

Q: II. Determine if the given pair of angles are coterminal or not coterminal. 1.) 90°, 430° 2.) -…

A: Since, you have asked multiple questions, according to our guidelines we will solve only three…

Q: Prove Proposition 59: Isosceles Triangle Theorem (expanded version of Proposition 40) A. A triangle…

A: Isosceles triangle states that opposite sides of a triangle are equal.

Q: (a) Define what it means for two triangles AABC and ADEF to be congruent. (b) State the SAS…

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Q: Which of the following statements are correct? Select all that apply. Only two of three angle…

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Q: Given that AE and DE are secants that intersect at point E outside the circle, prove AExBE = DExCE…

A: Given problem:- Given that AE and DE are secants that intersect at point E outside the circle, prove…

Q: Let A and B be distinct points. Write a proof of the following: AB n BA AB

A: To prove AB∩BA=AB¯ where AB and BA are both lines and A and B are distinct points.

Q: Point Q is the midpoint of ST. Which of the following is true about ST? ST = 2| QS - QT | O ST = QS…

A: Topic = Geometry Ture statement is  ST = QS + QT

Q: box 1: vertical angles congruence box 2: corresponding angles

A: Figure :

Q: 6. Which statement(s) are true about inscribed angles? Statement 1: The vertex of an inscribed angle…

A: Given that: Inscribed angle

Q: Prove Proposition 56: Incenter Theorem A. The angle bisectors of the triangle all intersect in a…

A: Note: As per our guidelines we are supposed to answer only 1️⃣ question. Kindly repost other…

Q: 7.) Write a conjecture using this information provided. If an angle is acute, it cannot be obtuse.…

A: Write the conjecture for the given statement

Q: Find a positive angle less than 360° that is coterminal with the given angle. 630° A positive angle…

A: Coterminal angle with 630° and less than 360°.

Q: 7. Use Pythagoras' theorem to determine whether this is a right triangle. 13 12

A: Given triangle: To determine: Using pythgorus we have to determine if the given triangle is a right…

Q: Write a proof for this form of Theorem 2-2. If two angles are supplements of congruent angles, then…

A: We have to prove the theorem

Q: 1. Use the Image below to determine what relationshlp exists between ZAGC and ZFGD. supplementary…

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Q: 1. Given that ZA, ZB, ZC, ZD e {angles} such that ZA and ZB are supplementary angles, ZC and ZD are…

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Q: Prove that the angle bisectors of alternate interior angles are parallel. Given: AB II CD, CB is the…

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Q: Prove the following statement. Given: - angle P and angle R are right angles. - M is the midpoint of…

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Q: Which of the following statements are correcte Select all that apply. 10 Only two of three angle…

A: Question :- which of the following statements are correct? Select all that apply.

Q: Find the measure of one interior angle of a regular 24-gon. Interior angle of the 24-gon is

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Q: Prove that a 40° angle is not constructible.

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Q: Which of the following are among the five basic postulates of Euclidea geometry? Check all that…

A: The Solution is given below

Q: Explain which theorems, definitions, or combinations of both can be used to prove that alternate…

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Q: Prove that two angles are complementury to the same angle, and then they are congruent to each…

A: Complementary angles: If two angles are complementary Then sum of their angles equal to 90°…

Q: (6) Prove the bisector of an angle A is the set of all points which are equidistant from the lines…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 6. Give the missing reasons in this proof of the Alternate Interior Angles Theorem 2 Given: I || n…

A: Please see the below picture for detailed solution.

Q: Find a positive angle less than 2π that is coterminal with the given angle.   22π/7

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Q: Which of the following is/are Euclid's axiom/s? I. All right angles are equal. II. One can describe…

A: We have to determine which of the following is Euclid's Axiom.

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.