← Previous 1 2 … 19 20 21 22 23 24 25 26 27 … 311 312 Next →
Isosceles triangles and share common side . is an obtuse triangle with sides . is also an obtuse isosceles triangle, where . What is the measure of ?Possible Answers:
Correct answer: Explanation: In order to prove triangle congruence, the triangles must have SAS, SSS, AAS, or ASA congruence. Here, we have one common side (S), and no other demonstrated congruence. Hence, we cannot guarantee that side is not one of the two congruent sides of , so we cannot state congruence with .
Points A and B lie on a circle centered at Z, where central angle <AZB measures 140°. What is the measure of angle <ZAB? Possible Answers:
Cannot be determined from the given information
Explanation: Because line segments ZA and ZB are radii of the circle, they must have the same length. That makes triangle ABZ an isosceles triangle, with <ZAB and <ZBA having the same measure. Because the three angles of a triangle must sum to 180°, you can express this in the equation: 140 + 2x = 180 --> 2x = 40 --> x = 20
Triangle FGH has equal lengths for FG and GH; what is the measure of ∠F, if ∠G measures 40 degrees? Possible Answers:
None of the other answers
Correct answer: 70 degrees Explanation: It's good to draw a diagram for this; we know that it's an isosceles triangle; remember that the angles of a triangle total 180 degrees. Angle G for this triangle is the one angle that doesn't correspond to an equal side of the isosceles triangle (opposite side to the angle), so that means ∠F = ∠H, and that ∠F + ∠H + 40 = 180, By substitution we find that ∠F * 2 = 140 and angle F = 70 degrees.
The vertex angle of an isosceles triangle is . What is the base angle?Possible Answers:
Correct answer: Explanation: An isosceles triangle has two congruent base angles and one vertex angle. Each triangle contains . Let = base angle, so the equation becomes . Solving for gives
In an isosceles triangle the base angle is five less than twice the vertex angle. What is the sum of the vertex angle and the base angle? Possible Answers:
Correct answer: Explanation: Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles. Let = the vertex angleand = base angleSo the equation to solve becomes or Thus the vertex angle is 38 and the base angle is 71 and their sum is 109.
Sides and in this triangle are equal. What is the measure of ?Possible Answers:
Correct answer: Explanation: This triangle has an angle of . We also know it has another angle of at because the two sides are equal. Adding those two angles together gives us total. Since a triangle has total, we subtract 130 from 180 and get 50.
An isosceles triangle has a base angle that is six more than three times the vertex angle. What is the base angle? Possible Answers:
Correct answer: Explanation: Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles. Let = vertex angle and = base angle.Then the equation to solve becomes
or .Solving for gives a vertex angle of 24 degrees and a base angle of 78 degrees.
The base angle of an isosceles triangle is thirteen more than three times the vertex angle. What is the difference between the vertex angle and the base angle? Possible Answers:
Correct answer: Explanation: Every triangle has . An isosceles triangle has one vertex ange, and two congruent base angles.Let be the vertex angle and be the base angle.The equation to solve becomes , since the base angle occurs twice.Now we can solve for the vertex angle. The difference between the vertex angle and the base angle is .
A particular acute isosceles triangle has an internal angle measuring . Which of the following must be the other two angles?Possible Answers:
Correct answer: Explanation: By definition, an acute isosceles triangle will have at least two sides (and at least two corresponding angles) that are congruent, and no angle will be greater than . Addtionally, like all triangles, the three angles will sum to . Thus, of our two answers which sum to , only is valid, as would violate the "acute" part of the definition.
In triangle ABC, Angle A = x degrees, Angle B = 2x degrees, and Angle C = 3x+30 degrees. How many degrees is Angle B? Possible Answers:
Explanation: Because the interior angles of a triangle add up to 180°, we can create an equation using the variables given in the problem: x+2x+(3x+30)=180. This simplifies to 6X+30=180. When we subtract 30 from both sides, we get 6x=150. Then, when we divide both sides by 6, we get x=25. Because Angle B=2x degrees, we multiply 25 times 2. Thus, Angle B is equal to 50°. If you got an answer of 25, you may have forgotten to multiply by 2. If you got 105, you may have found Angle C instead of Angle B.
← Previous 1 2 … 19 20 21 22 23 24 25 26 27 … 311 312 Next →
Avanti
Columbia University in the City of New York, Bachelor in Arts, Political Science and Government.
Yvan
Brigham Young University-Provo, Bachelor of Science, Mathematics Teacher Education.
Michelle
Florida International University, Bachelor in Arts, Political Science and Government.
If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.
If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors. Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org. Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney. Please follow these steps to file a notice: You must include the following: A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf. Send your complaint to our designated agent at: Charles Cohn Varsity Tutors LLC 101 S. Hanley Rd, Suite 300 St. Louis, MO 63105 Or fill out the form below: |