Welcome friends, in today's article where we will know about CPCT Full Form in Mathematics i.e. full form of CPCT in Mathematics and its meaning, so let's know without wasting time.
Cpct is a basic concept in Geometry. It is also called as Corresponding Angles Theorem.
In this article, we are going to discuss what are the CPCT. In different words, we will see how to find corresponding parts of congruent triangles in geometry.
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CPCT Full Form in Mathematics
Full Form of CPCT in Mathematics is "Corresponding Parts of Congruent Triangle".📐
CPCT Full Form in Mathematics in Hindi
हिंदी भाषा में यदि आप CPCT का गणितीय फुल फॉर्म जानना चाहते हैं तो वो होगा " सर्वांगसम त्रिभुज के संगत भाग (Corresponding Parts of Congruent Triangle)".
Corresponding Parts of Congruent
Meaning of CPCT | Meaning of CPCT in Mathematics :-
In a triangle, the sides and angles are congruent if they have the same size and measure. This means that corresponding parts have the same size and measure as well.
For example, in the diagram below, sides 'a' and 'b' are congruent (i.e., their measures are equal), so we can say that corresponding angles 'BAC' and 'CBD' are congruent (i.e., they have the same measure).
Theorem - Corresponding Angles Theorem
If two sides of one triangle are equal to two sides of another triangle, then all four angles of the first triangle will be equal to all four angles of the second triangle.
The three angles in two triangles having two sides and the included angle equal are called corresponding angles. The remaining two angles are called complementary angles. If the corresponding angles are equal, then they are congruent (equal).
Corresponding Parts of Congruent Triangle
Congruent triangles are triangles with the same angles and sides. Corresponding parts of congruent triangles are parts that are in the same position relative to each other.
Corresponding parts of congruent triangles include:
1) Angle bisectors, which are perpendicular lines through the angles of a triangle that divide each angle into two equal angles (half-angles).
The bisector of an angle is always half as long as the original angle's corresponding side. In a 30-60-90 triangle, for example, the bisector of 60 degrees is half as long as BC - one-half BC.
2) Medians, which are segments connecting the midpoints of two sides of a triangle. In an equilateral triangle (one with three equal sides), all three medians will have the same length - one-third of the length of any side.
In an isosceles triangle (one with two equal sides), only one median will be present - it will be half as long as either side. In an equiangular or scalene triangle (one with no equal sides), there will be no medians at all - only pairs of altitudes can serve this purpose).
CPCT Full Form in Maths Class 9
Importance of Corresponding Parts of Congruent Triangle:-
Corresponding Parts of Congruent Triangles The corresponding parts of congruent triangles are the pairs of corresponding angles and sides.
Theorem: If two triangles are congruent, then they have the following properties in common:
- Corresponding Angles are Equal.
- Corresponding Sides are Equal.
Example: Find the measure of angle PQR in each figure below.
A) (5x + 2y) degrees B) (2x + 3y) degrees C) (3x + 4y) degrees D) (-8x + 5y) degrees E) (-6x - 2y) degrees F) (-12x - 8y) degrees G) (-3x - 7y + 3z) degrees H) (5x + 10y + 2z - 3w - 6u - 5v + 4w + 9v - 12u - 6v + 7w + 4u).
Conclusion
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||Jai Hind||
Amazing information .
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