Table of Contents
- 1 What is the converse of Midpoint Theorem?
- 2 Are the sides of a triangle line segments?
- 3 What theorem can be used to find segment lengths in a triangle with a segment drawn parallel to a side of the triangle?
- 4 How do you determine if a triangle is valid?
- 5 How many triangles are formed from the mid points of a triangle?
- 6 How do you prove that a triangle is similar to itself?
What is the converse of Midpoint Theorem?
The converse of MidPoint Theorem The converse of the midpoint theorem states that ” if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side”.
Are the sides of a triangle line segments?
In a triangle, the sides of triangle are line segments. Therefore, the sides of the triangle are also written as , and mathematically. Similarly, the lengths of sides of a triangle are also expressed as the way the lengths of line segments are expressed in mathematics.
Can line segments make a triangle?
A triangle is a geometrical figure made of three sides, but the sides cannot take on any length. If the length of any one side is greater than the sum of the length of the other two, the line segments cannot be used to create a triangle.
How do you prove the midpoint of a proof?
Proof steps:
- AQ=QC [midpoint]
- ∠ APQ = ∠QRC [Corresponding angles for parallel lines cut by an transversal].
- ∠PBR=∠QRC=∠APQ [Corresponding angles for parallel lines cut by an transversal].
- ∠RQC=∠PAQ [When 2 pairs of corresponding angles are congruent in a triangle, the third pair is also congruent.]
What theorem can be used to find segment lengths in a triangle with a segment drawn parallel to a side of the triangle?
Midsegment Theorem
The Midsegment Theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.
How do you determine if a triangle is valid?
Approach: A triangle is valid if sum of its two sides is greater than the third side. If three sides are a, b and c, then three conditions should be met.
How do you prove a point is the midpoint of a segment?
Midpoint of a Line Segment
- Add both “x” coordinates, divide by 2.
- Add both “y” coordinates, divide by 2.
How do you prove that the line segments of a triangle?
Prove that the line segments joining the mid points of the sides of a triangle form four triangles, each of which is similar to the original triangle Given:* ∆ABC in which D, E, F are the mid-points of sides BC, CA and AB respectively. To Prove: Each of the triangles AFE, FBD, EDC and DEF is similar to ∆ABC.
How many triangles are formed from the mid points of a triangle?
Prove that the line segment joining the mid points of the sides of a triangle form four triangles, each of which is similar to the original triangle. Answer Given that:-
How do you prove that a triangle is similar to itself?
Prove that the line segments joining the midpoints of the sides of a triangle from four triangles each of which is similar to the original triangle. Prove that the line segments joining the midpoints of the sides of a triangle from four triangles each of which is similar to the original triangle.
Why are the smaller triangles of a parallelogram similar to each other?
The diagonal of a parallelogram divides the parallelogram into two congruent triangles. thus, mid points divide the triangle into 4 equal parts. Thus, the smaller triangles are congruent to each other and similar to the original triangle. Was this answer helpful?