Basic proportionality theorem: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio.
Where is basic proportionality theorem used?
Ans: The basic proportionality theorem helps to find the lengths of two sides. One of the applications of the basic proportionality theorem is finding the relationship of sides of two equiangular triangles.
How do you find the BPT theorem?
If P and Q are points on AB and AC such that AP = PB = 1/2 (AB) and AQ = QC = 1/2 (AC), then PQ || BC. Also, the converse of mid-point theorem is also true which states that the line drawn through the mid-point of a side of a triangle which is parallel to another side, bisects the third side of the triangle.
What does Thales theorem state?
In geometry, Thales’ theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ABC is a right angle. It is generally attributed to Thales of Miletus, but it is sometimes attributed to Pythagoras.
What is Thales theorem prove it?
Basic proportionality theorem (or) Thales theorem: If a line is drawn parallel to one side of a triangle intersecting the other two sides then it divides these sides in the same ratio. Given: A Δ ABC. A line DE is parallel to BC, meeting AB at D and AC at E. ∠ ABC = ∠ ADE ( Corresponding angles are equal.)
Is BPT and Thales theorem same?
What is another name of Basic proportionality theorem? Another name for BPT is Thales theorem. As per this theorem, If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.
What is the name of theorem 6.2 Class 10?
Theorem 6.2 – Converse of Basic Proportionality Theorem – Theorems.
How do you use BPT Theorem?
Thales Theorem Statement Let us now state the Basic Proportionality Theorem which is as follows: If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.
Why is Thales theorem important?
Thales of Miletus is credited with the discovery of 5 geometric theorems: A circle is bisected by its diameter. Angles opposite two equal sides of a triangle are equal. We can determine a triangle if we have the length of its base and two angles at the base are given.
What is another name for the BPT theorem?
Another name for BPT is Thales theorem. As per this theorem, If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio. What are the condition of two triangles to be similar? If two triangles are similar to each other then,
What is the basic proportionality theorem of a triangle?
3. 4. The basic proportionality theorem, also known as the Thales theorem states that “the line drawn parallel to one side of a triangle and cutting the other two sides divides the other two sides in equal proportion “. For example, in the given figure, line DE is drawn parallel to side BC, such that it joins the other two sides, AB and AC.
What is BPT in maths?
Here, we will state and prove BPT, which is the key to understand the above-stated concept introduced in similar triangles better. If a line is drawn parallel to one side of a triangle to intersect its other two sides in distinct points, then the other two sides are divided in the same ratio.
What is the converse of the BPT?
Also, the converse of the BPT, mid-point theorem also stands true. It states that the line drawn through the mid-point of a side of a triangle that is parallel to another side bisects the third side of the triangle.
