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In a triangle a segment is drawn joining the midpoint of two sides. What is true about the segment?
The triangle midpoint theorem states that the line segment is parallel to the third side and is congruent to one half of the third side.
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What of a triangle is a segment drawn through the midpoint of a side forming a right angle?
It is the perpendicular bisector
A median of a triangle is a line or segment that passes through a vertex and the side opposite that vertex?
A median of a triangle is a line or segment that passes through a vertex and the midpoint of the side opposite that vertex. The median only bisects the vertex angle from which it is drawn when it is an isosceles triangle.
Does a median of a triangle contain the midpoint of the side to which it is drawn?
Yes, the median of a triangle is from a vertex to the midpoint of the side opposite the vertex.
Which line ray or line segment is drawn from a triangles vertex to midpoint of the opposite side?
the median is drawn from the vertex to the midpoint of the opposite side
What types of concurrent constructions are needed to find the orthocenter of a triangle?
intersection of the lines drawn perpendicular to each side of the triangle through its midpoint
What is the Name of the triangle formed by joining of points formed by the perpendiculars drawn from vertexes to the opposite side?
isosceles triangle
What was Euclid's first postulate?
A straight line segment can be drawn joining any two points.
An altitude drawn to a side of a triangle passes through the midpoint of that side?
Not necessarily. That only happens in isosceles and equilateral triangles.
What is one difference between an altitude and a median of a triangle?
An altitude is a perpendicular drawn from a point to the opposite segment while a median is a segment drawn from a point to the opposite side such that it bisects the side.Altitudes and their concurrenceMedians and their concurrence
In an isosceles triangle does the median to the base bisect the vertex angle?
In the diagram, ABC is an isoscels triangle with the congruent sides and , and is the median drawn to the base . We know that ∠A ≅ ∠C, because the base angles of an isosceles triangle are congruent; we also know that ≅ , by definition of an isosceles triangle. A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side. That means ≅ . This proves that ΔABD ≅ ΔCBD. Since corresponding parts of congruent triangles are congruent, that means ∠ABD≅ ∠CBD. Since the median is the common side of these adjacent angles, in fact bisects the vertex angle of the isosceles triangle.
Are the medians of a triangle equidistant from each vertex?
Every triangle has three medians, just like it has three altitudes, angle bisectors, and perpendicular bisectors. The medians of a triangle are the segments drawn from the vertices to the midpoints of the opposite sides. The point of intersection of all three medians is called the centroid of the triangle. The centroid of a triangle is twice as far from a given vertex than it is from the midpoint to which the median from that vertex goes. For example, if a median is drawn from vertex A to midpoint M through centroid C, the length of AC is twice the length of CM. The centroid is 2/3 of the way from a given vertex to the opposite midpoint. The centroid is always on the interior of the triangle.
What are properties of the circumcenter of a triangle?
When a circle is drawn around a triangle touching each of its 3 vertices the circumcenter of the triangle is found by drawing 3 perpendicular lines at the midpoint of each of its sides and where these lines intersect within the triangle is its circumcenter.Apex: A. The circumcenter is equidistant from each vertex of the triangle. B. The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides. C. The circumcenter of an obtuse triangle is always outside it.
