Question

In: Advanced Math

Question: Prove the following: Claim: Consider a triangle ▵ABC and a point D on the interior...

Question:

  1. Prove the following:

Claim: Consider a triangle ▵ABC and a point D on the interior of segment BC. If σ(▵ABC) = 180, then σ(▵ABD) = σ(▵ACD) = 180.

Hint: Use the Split Triangle Theorem and/or the Split Quadrilateral Theorem

Solutions

Expert Solution


Related Solutions

Given triangle(ABC) with A-D-C, then BD < BA or BD < BC. Prove that the set...
Given triangle(ABC) with A-D-C, then BD < BA or BD < BC. Prove that the set consisting of a circle and its interior is a convex set.
let triangle ABC be a triangle in which all three interior angles are acute and let...
let triangle ABC be a triangle in which all three interior angles are acute and let A'B'C' be the orthic triangle. a.) Prove that the altitudes of triangle ABC are the angle bisectors of triangle A'B'C'. b.) Prove the orthocenter of triangle ABC is the incenter of traingle A'B'C'. c.) Prove that A is the A' -excenter of triangle A'B'C'.
plot each point and form the triangle ABC. Verify that the triangle ABC is a right...
plot each point and form the triangle ABC. Verify that the triangle ABC is a right triangle. Find its area. A= (-5, 10) B (2,7) C (-1,0)
Prove the following using the triangle inequality: Given a convex quadrilateral, prove that the point determined...
Prove the following using the triangle inequality: Given a convex quadrilateral, prove that the point determined by the intersection of the diagonals is the minimum distance point for the quadrilateral - that is, the point from which the sum of the distances of the vertices is minimal.
PROVE THE FOLLOWING RESULT: Using a compass and a straightedge, construct a triangle ABC such that...
PROVE THE FOLLOWING RESULT: Using a compass and a straightedge, construct a triangle ABC such that side BC is of length 2, the circumradius is of length 3/2 and the median AA' is of length 2 and is the midpoint of BC.
A triangle ABC has sides AB=50 and AC=10. D is mid-point of AB and E is...
A triangle ABC has sides AB=50 and AC=10. D is mid-point of AB and E is mid-point of AC. Angle bisector AG from vertex A meets side BC at G and divides it in 5:1 ratio. So BG=5 times GC. AG cuts ED at F. Find the ratio of the areas of the trapeziods FDBG to FGCE.
Prove Proposition 3.22(SSS Criterion for Congruence). Given triangle ABC and triangle DEF. If AB is congruent...
Prove Proposition 3.22(SSS Criterion for Congruence). Given triangle ABC and triangle DEF. If AB is congruent to DE, BC is congruent to EF, and AC is congruent to DF, then triangle ABC is congruent to triangle DEF. (Hint:Use three congruence axioms to reduce to the case where A=D, C=F, and points B and E are on opposite sides of line AC.)
1. Treacherous Triangle Trickery. Consider a charge distribution consisting of an equilateral triangle with a point...
1. Treacherous Triangle Trickery. Consider a charge distribution consisting of an equilateral triangle with a point charge q fixed at each of its vertices. Let d be the distance between the center of the triangle and each vertex, let the triangle’s center be at the origin, and let one of its vertices lie on the x-axis at the point x = −d. 1.1. Compute the electric field at the center of the triangle by explicitly computing the sum of the...
C. Prove the following claim, using proof by induction. Show your work. Let d be the...
C. Prove the following claim, using proof by induction. Show your work. Let d be the day you were born plus 7 (e.g., if you were born on March 24, d = 24 + 7). If a = 2d + 1 and b = d + 1, then an – b is divisible by d for all natural numbers n.
Consider an equilateral triangle, inscribed in a circle of radius a, with a point charge q...
Consider an equilateral triangle, inscribed in a circle of radius a, with a point charge q at each vertex. The electric field is zero at the center, but surprisingly there are three other points inside the triangle where the field is also zero. Where are they? Find the distance from these points to the center of the circle. Please just get the answer to E in terms of a, x, and y. I only need you to solve up to...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT