Prove that if a line bisects one side of a triangle and is parallel to a second side, then it bisects the third side.

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Q: A parallelogram must be a rectangle when its A diagonals are perpendicular B diagonals are congruent…

A: Given: A parallelogram  must be a rectangle when its diagonal A) diagonal are perpendicular…

Q: Which of the following would show that the diagonals of quadrilateral JKLM on the coordinate plane…

A: The given triangle JKLM is,

Q: Which construction of parallel lines is justified by the transversal and the corresponding angles…

A: Given: Theorem : " When two lines are intersected by a transversal and the corresponding angle are…

Q: Suppose that two lines are cut by a transversal in such a way that the pairs of corresponding angles…

A: If the transversal line N of two lines L and M, then formed angles ∠1 & ∠2 and ∠3 & ∠4 are…

Q: Prove that the figure formed by connecting consecutive midpoints of the sides of any quadrilateral…

A: Given   The figure formed by connecting consecutive midpoints of the sides of any quadrilateral

Q: Prove that C is on the perpendicular bisector of segment AB.

A: Consider the given vertices A-3,2, B5,-4, and C7,7. If C is on the perpendicular bisector of AB,…

Q: Can you determine if there’s enough info to prove the m is parallel to n? If so, which theorem would…

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Q: 2. Prove that the line joining the midpoint of a median to a vertex of the triangle trisects the…

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Q: Prove: In the five-point geometry, each point has exactly four lines on it.

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Q: Prove that if two lines are each perpendicular to a third line in the plane, then the two lines are…

A: Let slope of two lines are m1 and m2 and slope of third line is m3 . Now, as both lines are…

Q: . Prove that in a triangle, the orthocenter, centroid and the circumcenter are concurrent (in a…

A: Let X be the mid-point of EF Construct the median DX. Since G is the centroid, G is on DX by the…

Q: Show that the embedding of part (g) takes lines to "lines."

A: (h) We have to show that lines from ℝ2 maps to lines in P2. Lines in ℝ2 will be of the form ax+by=0.…

Q: Show that a quadrilateral is a parallelogram if one pair of its opposite sides are equal and…

A: Consider a quadrilateral whose one pair of its opposite sides are equal and parallel.

Q: In 3 Point Geometry, provide a proof that every line is on exactly two points.

A: To Prove: In 3-point geometry, every line is on exactly two points.

Q: Prove that C is on the perpendicular bisector of segment AB.

A: Solution:Given A(-4,-3), B(6,1) and C (5,-11)To Prove: C is perpendicular bisector of ABi.e., to…

Q: I need a paragraph proof for proving that a circle and a line cannot intersect in three or more…

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Q: Which construction of parallel lines is justified by the theorem “When two lines are intersected by…

A: *to find:- to find the correct diagram which justifies the given theorem.

Q: Prove that the sum of the squares of the lengths of the sides of a parallelogram is equal to the sum…

A: Let the sides of the parallelogram be 'l' with longest and 'b' with shortest parallel lines and…

Q: Prove that if A is a point on the perpendicular bisector of line segment BC then A is the same…

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Q: Prove that if two intersecting lines form one right angle, then they form four right angles.

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Q: Prove by the indirect method: “The length of a diagonal of a square is not equal in length to the…

A: Introduction: There are some basic methods that are used to prove any mathematical statement. These…

Q: prove that the midpoints of the sides of a quadrilateral of the mice are vertices of a…

A: We need to prove the midpoints of the sides of a quadrilateral of are vertices of a parallelogram.…

Q: a quadrilateral is a parallelogram if both pairs of its opposite sides are equal.

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Q: Prove that if the diagonals of a quadrilateral ABCD bisect each other, then ABCD is a parallelogram.

A: Here given that diagonals of quadrilateral bisect each other and we need to prove that the…

Q: Prove analytically that if the diagonals of a parallelogram rectangle. are equal, then the…

A: Given:-  Diagonals of parallelogram are equal.To proof  Parallelogram is a Rectangle.

Q: Prove that all the points on a perpendicular bisector of a line segment AB are equidistant from the…

A: Statement:All the points on a perpendicular bisector of a line segment AB are equidistant from the…

Q: Show that the median to the base of an isosceles triangle is perpendicular to base.

A: Introduction : We have asked to show that the median to the base of an isosceles triangle is…

Q: Prove that a parallelogram is a rectangle if and only if its diagonals are equal in length. (This…

A: Let ABCD be a parallelogram. Given AC and BD are diagonals of parallelogram in equal length. In…

Q: Determine if MN is parallel to JL 15 王 18

A: By basic proportionality therom if a line divides any two sides of triangle in same ratio then the…

Q: can a given line be in a two planes?in ten planes?

A: Yes,             The given statement is true;     A line can be drawn in a two planes ;…

Q: prove that there are exactly two lines parallel to a given line in Pappus' geometry

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Q: Let A, be the center of the square inscribed in acute triangle ABC with two vertice side BC (as…

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Q: Prove If a line is drawn parallel to one side of a triangle to intersect the other two points .The…

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Q: Prove that when the midpoints of consecutive sides of a quadrilateral are joined in order, the…

A: To prove: When the midpoints of consecutive sides of a quadrilateral are joined in order, the…

Q: Prove that all angles of parallelism are acute.

A: We need to prove, " All angles of parallelism are acute".

Q: When parallelograms are rectangles Prove that a parallelogram is a rectangle if and only if its…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: If B, I, and T are distinct points of a line and point I is between point B and T, if BI = 5 mm and…

A: Given- If B, I, and T are distinct points of a line and point I is between point B and T, if BI = 5…

Q: If two parallel lines AB and CD are intersected by transversal Im then, show that the quadrilateral…

A: The given figure is - Given that AB and CD are parallel. An quadrilateral is formed by the bisector…

Q: In a triangular space, every straight line, no tomb districts, are parallel i True false

A: The given statement is

Q: Prove: If two lines cut by a transversal form a pair of supplementary exterior angles on the same…

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Q: 3 -2-1 -2 -3 -4 -5 -6V How can we

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Q: Prove that the line segment joining the midpoints of two sides of a triangle determines a triangle…

A: Let draw the triangle △ABC  and the midpoints of the two sides as follows.

Q: Prove that parallel lines determine only one plane.

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Q: Prove that the line joining the midpoint of a median to a vertex of the triangle trisects the side…

A: Here ask to prove the line joining the midpoint of a median to a vertex of the triangle trisectsthe…

Q: Prove: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

A: Statement: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

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

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Q: If UV is not parallel to WX, what is m2X? U (142°

A: Trapezium Angles  For a regular or isosceles trapezium, the sets of angles adjoined by parallel…

Q: Suppose you are given a line l and a triangle AABC such that A, B, and C do not lie on l. Prove that…

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Q: A diagonal may be inserted onto a diagram of a parallelogram to complete a proof involving the…

A: A parallelogram is a closed figure with 2 pairs of opposite sides parallel to each other.