Advertisements
Advertisements
प्रश्न
In the given figure, AB = DB and AC = DC. Find the values of x and y.
Advertisements
उत्तर
In ΔABC and ΔDBC
AB = DB ....[given]
AC = DC ....[given]
BC = BC ....[common]
∴ By Side-Side-Side criterion of congruence,
ΔABC ≅ ΔDBC
∴ ∠ACB =∠DBC ....[c.p.c.t]
⇒ y + 15° = 63°
⇒ y = 63° - 15°
⇒ y = 48°
Now, ∠ABC = ∠DBC ....[c.p.c.t]
⇒ 29° = 2x - 4°
⇒ 2x = 29° + 4°
⇒ 2x = 33°
⇒ x = `(33°)/(2)`
⇒ x = 16.5°
Hence, x = 16.5° and y = 48°.
APPEARS IN
संबंधित प्रश्न
In the given figure, if AB = AC and ∠B = ∠C. Prove that BQ = CP.
In triangles ABC and PQR, if ∠A = ∠R, ∠B = ∠P and AB = RP, then which one of the following congruence conditions applies:
If ΔPQR≅ ΔEFD, then ∠E =
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°.
On the sides AB and AC of triangle ABC, equilateral triangle ABD and ACE are drawn. Prove that:
- ∠CAD = ∠BAE
- CD = BE
In a triangle, ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB. Prove that: AD = CE.
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(∠B = 70°,BC = 6cm,∠C = 50°);
ΔXYZ;(∠Z = 60°,XY = 6cm,∠X = 70°).
In ΔABC, AB = AC and the bisectors of angles B and C intersect at point O.Prove that BO = CO and the ray AO is the bisector of angle BAC.
O is any point in the ΔABC such that the perpendicular drawn from O on AB and AC are equal. Prove that OA is the bisector of ∠BAC.
“If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent.” Is the statement true? Why?
