Advertisements
Advertisements
प्रश्न
ABC is a triangle in which ∠B = 2 ∠C. D is a point on BC such that AD bisects ∠BAC and AB = CD.
Prove that ∠BAC = 72°.
Advertisements
उत्तर
In ΔABC,
∠B = 2∠C or, ∠B = 2y, where ∠C = y.
AD is the bisector of ∠BAC.
So, let ∠BAD = ∠CAD = x.
Let BP be the bisector of ∠ABC. Join PD.
In ΔBPC, we have
∠CBP = ∠BCP = y ⇒ BP = PC
In Δ′s ABP and DCP, we have
∠ABP = ∠DCP,
∠ABP = ∠DCP = y
BP = PC ........(As proved above)
∠ADC = ∠ABD + ∠BAD
⇒ x + 2x = 2y + x
⇒ x = y
APPEARS IN
संबंधित प्रश्न
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.
ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle.
Determine the measure of each of the equal angles of a right-angled isosceles triangle.
AB is a line seg P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See Fig. 10.26). Show that the line PQ is perpendicular bisector of AB.
PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. Prove that PS = PT.
ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
Which of the following statements are true (T) and which are false (F):
Sides opposite to equal angles of a triangle may be unequal
Which of the following statements are true (T) and which are false (F):
The measure of each angle of an equilateral triangle is 60°
Which of the following statements are true (T) and which are false (F):
The two altitudes corresponding to two equal sides of a triangle need not be equal.
Fill the blank in the following so that the following statement is true.
Sides opposite to equal angles of a triangle are ......
Fill the blank in the following so that the following statement is true.
In an equilateral triangle all angles are .....
Fill the blank in the following so that the following statement is true.
In a ΔABC if ∠A = ∠C , then AB = ......
In Fig. 10.131, prove that: (i) CD + DA + AB + BC > 2AC (ii) CD + DA + AB > BC
Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than twice the median drawn to the third side.
Fill in the blank to make the following statement true.
In a right triangle the hypotenuse is the .... side.
Fill in the blank to make the following statement true.
If two angles of a triangle are unequal, then the smaller angle has the........ side opposite to it.
Fill in the blank to make the following statement true.
If two sides of a triangle are unequal, then the larger side has .... angle opposite to it.
In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.
In the given figure, x + y =
In the given figure, AB and CD are parallel lines and transversal EF intersects them at Pand Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°, then
