Answered: (4) Prove that if two altitudes in a…

Math

Algebra

(4) Prove that if two altitudes in a triangle are congruent, then the triangle is Isosceles.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.CR: Review Exercises

Problem 35CR: Prove the statements in Review Exercises 32 to 36 using analytic geometry. If two medians of a...

See similar textbooks

Related questions

Q: Show that the triangle with vertices P(6, ; 7), Q(11, ; 3) and R(2, ; 2) is a right -angled triangle…

Q: Show that the points (a,a),(-a,-a) and (-V3a, v3a) are the За vertice of an equilateral triangle.…

A: Given the co-ordinate of a triangle Let A=(a,a)B=(−a,−a)C=(−3a,3a)

Q: How would the following triangle be classified?

A: Two side lengths are congruent and one angle measures 90 degree

Q: 3. Complete the proof of the Triangle Exterior Angle Conjecture own words.

Q: 2. Prove that if the Fermat-Torricelli point of an acute triangle ABC coincides with the incenter,…

Q: Prove that in any triangle, the lines joining the endpoints of the three medians form a triangle…

A: Lemma: In ∆ABC:Using this lemma we can say that From 1: ADAB = DFBC=> DFBC = 12 ---------aFrom 2:…

Q: Draw two triangles ABC and A'B'C' on different planes such that the two triangles are perspective…

A: We need to draw two triangles such that the two triangles are perspective from a line and from a…

Q: Show that the points (-2, 4), (3, -1), (-1, -3) are the vertices of an isosceles triangle, and find…

A: Let the given points be - A = -2, 4B = 3, -1C = -1, -3Now, Let's find the distance AB between point…

Q: Show that the triangle whose vertices are A(3, 6), B( - 6, 4), and C(1, - 2) is an isosceles…

A: to show that triangle is isosceles.

Q: side

Q: Excercise 9 Prove that the bisectors of the interior angles of a triangle are concurrent at a point…

A: Let ABC be a triangle We first make two angle bisectors and then prove third line from the…

Q: Prove: If the ray that bisects an angle of a triangle is perpendicular to the side that it…

A: To prove if the ray that bisects an angle of a triangle is perpendicular to the side that it…

Q: A_______ __________ is a positive angle whose vertex is at thecenter of a circle

A: It is given that, A_______ __________ is a positive angle whose vertex is at thecenter of a circle.

Q: By calculating the lengths of its sides, show that the triangle with vertices at the points A(1, 2),…

Q: In hyperbolic geometry, prove that the Omega triangles ABΩ and A′B′Ω′ are congruent if the pair of…

Q: 1. Prove analytically that if A and B are the ends of a diameter of a circle and C is any point on…

Q: Consider a right triangle whose two short sides have lengths of 5 and 12 feet, respectively. Then…

Q: On a coordinate plane, triangle FGH is formed with the vertices at point F(4, 2), point G(4, 6), and…

A: We have given that F(4, 2), G(4, 6) and H(6, 4).

Q: all triangles are convex. true or false?

A: A convex polygon is defined as a polygon with all its interior angles less than 180°. This means…

Q: Prove that if a line bisects one side of a triangle and is parallel to a second side, then it…

A: Basic proportionality Theorem of triangle is define as if a line drawn parallel to one side of…

Q: Are these triangles similar? If so, which theorem can be used to prove your answer? Yes No

A: given triangle are similar

Q: Prove that the sum of the angles of an elliptical triangle is more than two right angles.

A: Solution:-

Q: 2. It is possible for two angles of a triangle in the hyperbolic plane to each have a measure of 2.

A: Solution

Q: CONSTRUCT EQUILATERAL TRIANGLE UPON AB AS THE BASE. At

A: According to question given thatAB is the base of the equilateral triangle and we have to construct…

Q: Prove that the measure of an exterior angle of a triangle is equal to the sum of the measures of two…

Q: Your friend claims that the SAS Congruence Theorem (Theorem 5.5) will apply to a triangle and its…

A: It is known that the triangle that is obtained after translated, reflected, rotated, and dilated…

Q: Use Ceva's Theorem to prove that the altitudes of an acute triangle are concurrent.

A: The converse of ceva's theorem states that if the product of the ratios of the division of the three…

Q: An isosceles right triangle has one Vangle and equal sides.

A: our objective is to find the statement.

Q: Prove that a quadrilateral can be inscribed in a circle if and only if its opposite angles are…

Q: Prove that the sum of the angles of a hyperbolic triangle is less than 180 degrees and explain.

Q: Theorem 78 states that if the radius of a circle is r, its area is πr2. true or false

A: In the statement, it is asked if the area of circle is ∏r2

Q: Prove the Pythagorean Theorem with Similar Triangles using a two-column proof.

A: To Prove the Pythagorean Theorem with Similar Triangles using a two-column proof

Q: How to prove congruent triangles

Q: Prove that if two triangles have congruent bases, then their areas are in the same ratio as their…

A: To show that the ratio of the areas is equal to the ratio of the heights, if the two triangles have…

Q: Show that triangle with vertices p(6,-7),q(11,-3) and R(2,-2) is a right angled triangle using…

A: We first find the length of the sides using the distance formula.…

Q: 34. Prove that an altitude of an acute scalene triangle cannot bisect the angle from whose vertex it…

A: We will prove that an altitude cannot bisect the angle from whose vertex it is drawn as following.…

Q: Show that the triangle with vertices A(0, 0), B(1, √3), and C(2, 0) is equilateral.

Q: 44. Prove: The diagonals of an isosceles trapezoid are congruent.

Q: Show that a triangle whose sides are of lengths 5, 12, and 13 is a right triangle. Identify the…

A: Given: Show that a triangle whose sides are of lengths 5, 12, and 13 is a right triangle.Identify…

Q: Show that if a line is drawn from the vertex of an isosceles triangle that bisects the base of the…

A: Let ABC is an isosceles triangle such that AB=AC. Let AD is the bisector of angle A. To prove BD=BC…

Q: equiangular isosceles triangle?

Q: Prove that if a point is contained in two angles of a triangle, then it is contained in the interior…

A: In a triangle, any two angles are adjacent (i.e, sharing a common hand)

Q: A triangle is inscribed in a rectangular hyperbola s to the opposite side. Prove that the trian…

Q: Use the Pythagorean Theorem's converse to prove that a triangle with sides of lengths 11,60, and 61…

Q: Show that p = V2/1 - cos O in an isosceles triangle that has two sides of length p, an angle of 0…

A: This question is based on application of Cosine rule.

Q: Prove analytically that the perpendicular bisector of the sides of a triangle are concurrent.

Q: Prove that the altitudes of a triangle are concurrent.

Q: Construct an equilateral triangle & a square from a wire of 100m together, such that their area is…

Question

100%

(4) Prove that if two altitudes in a triangle
are congruent, then the triangle is Isosceles.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Basics (types, similarity, etc)$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

What type of trapezoid a has congruent diagonals. b has congruent base angles.
Prove that the altitude drawn to the hypotenuse of a right triangle separates the right triangle into two right triangles that are similar to each other and to the original right triangle.
a To locate the orthocenter, is it necessary to construct all three altitude of a right triangle? b What point is the orthocenter of any right triangle?
Classify as true or false: a If the vertex angles of two isosceles triangles are congruent, the triangles are similar. b Any two equilateral triangles are similar.
a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle. Use the fact that the congruent diagonals of a rectangle bisect each other. Be sure to provide a drawing. bUse the relationship from part a to find CM, the length of the median to the hypotenuse of right ABC, in which mC=90, AC = 6, and BC = 8.
What is the general name of the point of concurrence for the three altitudes of a triangle?
a Is it really necessary to construct all three bisectors of the angles of a triangle to locate its incenter? b Is it really necessary to construct all three perpendicular bisectors of the sides of a triangle to locate its circumcenter?
On a piece of paper, use your compass to construct a triangle that has two sides of the same length. Cut the triangle out of the paper and fold the triangle in half so that the congruent sides coincide one lies over the other. What seems to be true of two angles of that triangle?
Circles O, P, and Q are tangent as shown at points X, Y, and Z. Being as specific as possible, explain what type of triangle PQO is if: a OX=2,PY=3,QZ=1 b OX=2,PY=3,QZ=2
Prove the statements in Review Exercises 32 to 36 using analytic geometry. If two medians of a triangle are equal in length, then the triangle is isosceles.
Two sets of rails railroad tracks are equally spaced intersect but not at right angles. Being as specific as possible, indicate what type of quadrilateral WXYZ is formed.