Advertisements
Advertisements
प्रश्न
If the following pair of the triangle is congruent? state the condition of congruency:
In ΔABC and ΔPQR, BC = QR, ∠A = 90°, ∠C = ∠R = 40° and ∠Q = 50°.
Advertisements
उत्तर
In ΔPQR
∠R = 40°, ∠Q = 50°
∠P + ∠Q + ∠R = 180° ...[Sum of all the angels in aa triangle = 180°]
⇒ ∠P + 50° + 40° = 180°
⇒ ∠P + 90° = 180°
⇒ ∠P = 180° - 90°
⇒ ∠P = 90°
In ΔABC and ΔPQR
∠A = ∠P
∠C = ∠R
BC = QR
By Angle-Angle-Side criterion of congruency, the triangles
ΔABC and ΔPQR are congruent to each other.
∴ ΔABC ≅ ΔPQR
APPEARS IN
संबंधित प्रश्न
In a squared sheet, draw two triangles of equal areas such that
The triangles are congruent.
What can you say about their perimeters?
In the given figure, ABC is a triangle in which ∠B = 2∠C. D is a point on side BC such that ADbisects ∠BAC and AB = CD. BE is the bisector of ∠B. The measure of ∠BAC is
In the following example, a pair of triangles is shown. Equal parts of triangles in each pair are marked with the same sign. Observe the figure and state the test by which the triangle in each pair are congruent.
By ______ test
Δ ABC ≅ ΔPQR
State, whether the pairs of triangles given in the following figures are congruent or not:
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
(iii) AC bisects angle DCB
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(BC = 5cm,AC = 6cm,∠C = 80°);
ΔXYZ;(XZ = 6cm,XY = 5cm,∠X = 70°).
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 5cm,BC = 7cm,CA = 9cm);
ΔKLM;(KL = 7cm,LM = 5cm,KM = 9cm).
In the figure, RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT.
Prove that in an isosceles triangle the altitude from the vertex will bisect the base.
If AB = QR, BC = PR and CA = PQ, then ______.
