Congruence of Triangle 1.pptx Maths, Triangles for GRADE 8
- 1. CONGRUENCE OF TRIANGLE PRE-ASSESSMENT: 1.Name the elements of triangle ABC: 2. Sum of the measure of all angles of a triangle is _____.
- 2. ANGLE SUM PROPERTY OF A TRIANGLE Sum of all angles of a triangle is 1800 Consider a ABC A B C Name the three angles of ABC BAC ,ABC & ACB BAC ABC ACB + + = 1800 In ABC,
- 3. is called a triangle A B C SIDES : side AB, side BC, side AC ANGLES : BAC, ABC, ACB Three sided closed figure Elements of triangle : CONGRUENCE OF TRIANGLE
- 4. Triangles B A C A + B + C = 180 o M N P A B C To understand the concept of congruence and corresponding parts. Learning Objective:
- 5. Figures having SAME SHAPE SAME SIZE AND
- 6. SAME SIZE CONGRUENT FIGURES SAME SHAPE and =
- 7. 1)If two line segments have equal length, they are congruent. Conversely, if two line segments are congruent, they are of equal length. Every line segment is congruent to itself. Example: If seg AB=5cm and seg PQ=5cm Then we can say seg AB ≅ Seg PQ CONGRUENCE OF SIMPLE GEOMETRICAL SHAPES 2) If two angles have the same measure, they are congruent. Conversely, if two angles are congruent, they have equal measure. Every angle is congruent to itself. we can say that ∠ABC is congruent to ∠MNO and we write it as ∠ABC ≅∠MNO. If m∠ABC = m∠MNO
- 8. CONGRUENT FIGURES What do you observe ? One circle exactly fits into the other i.e. they coincide Let us place a circle over the other.. Such figures are called congruent figures Observe..
- 9. A B C P Q R ABC PQR Pairs of equal angles A = P B = Q C = R Pairs of equal sides AB PQ BC QR AC PR What did you observe ? They coincide So, what can we say about ABC and PQR ? ABC is congruent to PQR CONGRUENT TRIANGLES Since the triangles are congruent, the angles and sides of one triangle will be equal to the corresponding angles and sides of the other triangle So, let us first write the pairs of equal angles Now, let us write the pairs of equal sides
- 10. CONGRUENCE OF TRIANGLES Two triangles are said to be congruent, if the six elements, that is, three sides and three angles of the first triangle are equal to the corresponding six elements of the other triangle. In the two triangles ABC and PQR, if AB = PQ, BC = QR and AC = PR and ∠A = ∠P,∠B = ∠Q and ∠C = ∠R, then ΔABC ≅ΔPQR
- 11. Guided Practice Example 1: Without drawing the triangles, state the correspondence between the sides and the angles of the following pairs of congruent triangles. a)ΔABC ≅ΔDEF b)ΔABC ≅ΔEFD
- 12. Solution Solution: a)Given that ΔABC ≅ΔDEF So, A↔D, B↔E and C↔F Therefore, AB↔DE, BC↔EF and AC↔DF. Also, ∠A↔ ∠D,∠B↔ ∠E and ∠C↔ ∠F. b)Given that ΔABC ≅ΔEFD So, A↔E, B↔F and C↔D Therefore, AB↔EF, BC↔FD and AC↔ED. Also, ∠A↔ ∠E, ∠B↔ ∠F and ∠C↔ ∠D .Note: ABC↔ DEF and ABC↔EFD are two correspondences by which ΔABC and ΔDEF can be congruent, but there can be other correspondences also.
- 14. Challenges If ΔPQR and ΔXYZ are congruent under the correspondence QPR↔XYZ, then which of the following is false (a) ∠R=∠Z ,QR=XZ (b) PQ=YX and PR=YZ (c) ∠P=∠Y and QR= YZ (d) ∠Q=∠X Without drawing the triangles, state the correspondence between the sides and the angles of the following triangles. a) ΔPQR ≅ΔABC b) ΔPQR ≅ΔBCA Level 2: Level 3:
- 15. Daily assessment Which of these is not true if two circles have the same diameter? a) They have the same area b) They have the same radius c) They are congruent d) They have the same centre
- 16. Home work Complete the following statements. a) Two line segments are congruent if _____ b) Among two congruent angles, if one angle has a measure of 60°, the measure of the other angle is _________