Advertisements
Advertisements
Question
In ∆PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is ______.
Options
4 cm
5 cm
2 cm
2.5 cm
Advertisements
Solution
In ∆PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is 4 cm.
Explanation:
Given, ∆PQR such that ∠R = ∠P, QR = 4 cm and PR = 5 cm
In ∆PQR, ∠R = ∠P
⇒ PQ = QR ...[Sides opposite to equal angles are equal]
⇒ PQ = 4 cm ...[∵ QR = 4 cm]
Hence, the length of PQ is 4 cm.
APPEARS IN
RELATED QUESTIONS
Show that the angles of an equilateral triangle are 60° each.
In figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD
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.
In Fig. 10.40, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT
Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.
The vertical angle of an isosceles triangle is 100°. Find its base angles.
ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that ΔABC is isosceles
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.
Prove that the perimeter of a triangle is greater than the sum of its altitudes.
Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than the third side.
Fill in the blank to make the following statement true.
Difference of any two sides of a triangle is........ than the third side.
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 a ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =
In the given figure, what is z in terms of x and y?
In the given figure, what is y in terms of x?
In the given figure, if BP || CQ and AC = BC, then the measure of x is
In ∆ABC, BC = AB and ∠B = 80°. Then ∠A is equal to ______.
ABC is an isosceles triangle with AB = AC and D is a point on BC such that AD ⊥ BC (Figure). To prove that ∠BAD = ∠CAD, a student proceeded as follows:
In ∆ABD and ∆ACD,
AB = AC (Given)
∠B = ∠C (Because AB = AC)
and ∠ADB = ∠ADC
Therefore, ∆ABD ≅ ∆ACD (AAS)
So, ∠BAD = ∠CAD (CPCT)
What is the defect in the above arguments?
[Hint: Recall how ∠B = ∠C is proved when AB = AC].
Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD
