Advertisements
Advertisements
Question
In the given figure, if AC is bisector of ∠BAD such that AB = 3 cm and AC = 5 cm, then CD =
Options
2 cm
3 cm
4 cm
5 cm
Advertisements
Solution
It is given that
AC, is bisector of ∠BAD
∠BAC = ∠CAD
AB = 3cm
AC =5cm
We are to find the side CD
Analyze the figure and conclude that
CD = BC (As in the two triangles are congruent)
In ΔABC
`BC = sqrt25- 9`
`= sqrt 16`
= 4
So
BC = CD
⇒ CD = 4
Hence (c) CD = 4.
APPEARS IN
RELATED QUESTIONS
In triangles ABC and PQR, if ∠A = ∠R, ∠B = ∠P and AB = RP, then which one of the following congruence conditions applies:
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, then the measure of vertex angle of the triangle is
In the given figure, X is a point in the interior of square ABCD. AXYZ is also a square. If DY = 3 cm and AZ = 2 cm, then BY =
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
As shown in the following figure, in ΔLMN and ΔPNM, LM = PN, LN = PM. Write the test which assures the congruence of the two triangles. Write their remaining congruent parts.
In the given figure, ∠P ≅ ∠R seg, PQ ≅ seg RQ. Prove that, ΔPQT ≅ ΔRQS.
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 ΔPQR, LM = MN, QM = MR and ML and MN are perpendiculars on PQ and PR respectively. Prove that PQ = PR.
If the given two triangles are congruent, then identify all the corresponding sides and also write the congruent angles
If ∆PQR is congruent to ∆STU (see figure), then what is the length of TU?
