Advertisements
Advertisements
प्रश्न
In two right triangles one side an acute angle of one are equal to the corresponding side and angle of the othe Prove that the triangles are congruent.
Advertisements
उत्तर
Given that, in two right triangles one side and acute angle of one are equal to the corresponding side and angles of the other.
We have to prove that the triangles are congruent. Let us consider two right triangles such that
∠B = ∠C = 90° ........(1)
AB = DE ........(2)
∠C = ∠F ........(3)
Now observe the two triangles ABC and DEF
∠.C = ∠F [From (3)]
∠B = ∠E [From (1)]
and AB = DE [From (2)]
So, by AAS congruence criterion, we have
ΔABC ≅ ΔDEF
∴The two triangles are congruent Hence proved
APPEARS IN
संबंधित प्रश्न
If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to `bar(DF)`
Find the measure of each angle of an equilateral triangle.
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
Observe the information shown in pair of triangle given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.
From the information shown in the figure,
In ΔABC and ΔPQR
∠ABC ≅ ∠PQR
seg BC ≅ seg QR
∠ACB ≅ ∠PRQ
∴ ΔABC ≅ ΔPQR ...`square` test
∴ ∠BAC ≅ `square` ...corresponding angles of congruent triangles.
`{:("seg AB" ≅ square),("and" square ≅ "seg PR"):}}` ...corresponding sides of congruent triangles
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°.
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(∠B = 90°,BC = 6cm,AB = 8cm);
ΔPQR;(∠Q = 90°,PQ = 6cm,PR = 10cm).
In ΔABC, AD is a median. The perpendiculars from B and C meet the line AD produced at X and Y. Prove that BX = CY.
In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆PQR should be equal to side AB of ∆ABC so that the two triangles are congruent? Give reason for your answer.
In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆PQR should be equal to side BC of ∆ABC so that the two triangles are congruent? Give reason for your answer.
Two figures are congruent, if they have the same shape.
