Triangles Test ...

If in the given figure, ΔABC ~ ΔCDA, then = ?

In ΔBAC, BA = BC and CD bisects ACB. Also if CA = CD, find BAC - ABC.

In rectangle ABCD, AB² + BC² + CD² + DA² = ?

In the given figure, area of ΔCQP is 32 cm², which is equal to the area of ΔCQR, and AQ = 6 cm. What is the value of AB?

In the given adjacent figure, ABC = AED = 90°, AE = 8 cm, AB = 12 cm , AD = (2x + 6) cm, and AC = (4x + 2) cm. Find AD and AC.

In the given figure, DEB = ACB. What is equal to?

In the given figure, RN and QM are perpendicular to PQ and PR, respectively. If PR = 12 cm, PQ = 10 cm and QM = 8 cm, then what is the value of 10RN?

In the given figure, AD = DC and ADB = CDB.


Which of the following criteria will make ΔADB congruent to ΔCDB?

In the given figure, DE is parallel to BC, FE is parallel to DC, BC = 10 cm, and DE = 6 cm. Find 6FD.

In the following figure, AB and CD are perpendicular to BD. Find the length of side AC.

In the given figure, ST || PR and SR || PA. What will be the value of QA – QR, if QT = 3 cm and TR = 9 cm?

In the given figure, MNO and OPM are isosceles right triangles. What is the length of OP?

In ΔABC, right-angled at B, AD = AE and CF = CE. If DEF is equal to x, find the value of x.

Sima is sliding down a slide in a park, which is in the shape of a right-angled triangle. She slides down with a length of A m and then returns back to the slide by climbing up with a perpendicular length of B m. If A - B = 2 m, find out the length of the base of the slide in terms of A.

In a ΔMQR, QT ⊥ MR, PQ = QR, and QP is a line that touches MR. Which of the following option is correct?

Arpan starts moving from the foot of the tower (height 8 m) on the ground, covers 4 m and stops at point C for some time. Then, he again starts moving in the same direction, further covers 11 m, and marks that point as D. What is the approximate difference between the distance of the top of the tower from point D and from point C?

In the sextant experiment, the distance between the top of the two buildings on the plane ground comes out to be 5 m. If the height of the two buildings is 16 m and 13 m, what is the distance between the two buildings?

In the given figure, DF || AG, DE || AB, AB = 15, CD = 8, AD = a, DE = 10, FG = b and CG = 6. The ratio a : b is equal to

In a triangular field, three players A, B and C are standing in the corners of the field. The distance of player A from player C is same as the distance of player A from B. The distance of player B from player C is 30 m and the perpendicular distance of player A from his front side CB is 30 m. If the distance between the points D and E marked on the triangular field is 14 m and the line from D to E is parallel to the line CB, then what is the distance between player A and the midpoint of the line DE?

There are two buildings, A and B, standing parallel to each other. Height of building A is 6 m and that of building B is 17 m. A ribbon is used to connect the foot of building B to the top of building A, whose length is 10 m. Another ribbon is used to connect the top of building B to the foot of building A. Both ribbons cross each other at some point.

(i) What is the distance between the feet of building A and building B?
(ii) What is the perpendicular distance from the ground to the point where ribbons cross, if the distance of that point on ground from the foot of building B is 6 m?

Match the following:

Column I	Column II
(A) In ΔPQR and ΔMNO, if P = M, Q = N, then ΔPQR ~ ΔMNO.	(I) Basic Proportionality Theorem (BPT)
(B) If a line is parallel to a side of a △ which intersects the other two sides into two distinct points, then the line divides those sides in proportion.	(II) SAS Similarity Criterion
(C ) If in two triangles, one pair of corresponding sides are proportional and the included angles are equal, then the two triangles are similar.	(III) AA Similarity Criteria
(D) In ΔXYZ and ΔLMN, XZ = 6 cm, YZ = 7 cm, XY = 8 cm, LM = 24 cm, LN = 18 cm, and MN = 21 cm, then ΔXYZ ~ ΔLMN.	(IV) SSS Similarity Criteria

Which of the following statements is correct?

(A) If all the corresponding sides of ΔABC and ΔPQR are equal, the triangles are congruent.
(B)

In the above picture, only shape I and II are similar because the ratio of corresponding sides is equal.

(C) A pair of similar triangles has three equal angles and proportional sides.
(D)

The triangles are congruent, according to SAS.

In the given figure, PS is a median of ΔPQR, and PM is perpendicular to QR. Find:
(i) PR²
(ii) PQ²

In the figure above, QRS is an equilateral triangle and QTS is an isosceles triangle. If a = 13°, then what is the value of b?

In triangle ABC, ∠C and in triangle PQR, ∠R are 90°. If A = P, DQ = 2.5 cm and AD is the perpendicular bisector of QP, then find the length of AB.