Criteria for Congruency of Triangles

Q. Which of the following is not a criterion for congruence of triangles?

(a) SAS

(b) SSA

(c) ASA

(d) SSS

Q. In ∆ABC and ∆PQR , AB=PQ , BC=QR CB and RQ are extended to X and Y respectively and ABX = PQY Prove that ∆ABC is congruent to ∆PQR

Q. In Fig 4, OC is drawn perpendicular from the centre O of the circle to the chord AB. OB =5 cm and OC =3 cm, then the length of the chord AB is

Q.

A circle with center O and radius = 5 cm has two chords AB and AC, such that AB = AC = 6 cm. If by joining B and C the line segment passes from the center of the circle O, then what is the length of BC?

1. 5 cm
2. 9 cm
3. 10 cm
4. 8cm

Q.

A circle of radius 3 cm can be drawn through two points A, B such that AB = 6cm

1. True

2. False

Q.

Choose the correct answer in each of the following:

Which of the following is not a criterion for congruence of triangles?

(a) SSA (b) SAS (c) ASA (d) SSS

Q.

What do you mean by the included angle/side of a triangle? What is the difference between ASA and AAS criteria for congruency of traingles

Q.

If I draw a circle on a tracing paper and draw two equal chords and drop perpendicular from centre to the chord. Fold the paper such that the two chords coincide. Then, the two perpendiculars are also coinciding.

1. True

2. False

Q. Let A , B, C be sets such that A $\cap$ B $\ne \varphi$, B $\cap$ C $\ne \varphi$ and A $\cap$ C $\ne \varphi$ . Do you claim that A $\cap$ B $\cap$ C $\ne \varphi$? Justify your answer.

Q.

In figure , if OA = OB, OD= OC then ∆AOD ≅ ∆BOC by congruence rule:

1. ASA

2. SSS

3. SAS

4. RHS

Q.

In the given figure, ABC is a triangle, right-angled at B. BCDE is a square on the side BC and ACFG is a square on AC. Then,

1. $AD=BF$

2. $AD>BF$

3. $AD<BF$

4. lengths of sides AD and BF cannot be compared.

Q. Question 5
Write True or False and justify your answer :

A circle of radius 3 cm can be drawn through two points A, B such that AB = 6cm.

Q. Prove that the diagonals of square divide it into four congruent triangles.

Q.

Which of the following data is not necessary for construction of triangle ABC with base BC by the method of Triangle Construction 1?

1. either option angle B or angle A

2. BC's length

3. Angle B

4. Angle C

Q.

In figure P, Q are points on sides AB, AC respectively of ∆ABC such that ar (BCQ) = ar (BCP). Then,

1. PA || BC

2. PQ || BC

3. AB || CP

4. BP || QC

Q.

ABC and BDE are two equilateral triangles such that D is the mid point of BC. AE intersects BC in F. Then ar (BDE) is equal to

1. 2ar (ABC)

2. ¹/₄ ar (ABC)

3. ar (ABC)

4. ¹/₂ ar (ABC)

Q.

In the following diagrams, ABCD is a square and APB is an equilateral triangle.

In each case, $\Delta APD\cong \Delta BPC$.

State whether the above statement is true or false.

1. True
2. False

Q. Which of the following is not the criterion for congruence of triangles? a) SAS b)SSA c) ASA d) SSS

Q.

In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then find the distance of OD.

Q.

Match the two columns:
$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(A) The radius of a circle is 8 cm and}& \text{(p) 23 cm}\\ \text{the length of one of its chords is 12 cm.}& \\ \text{the distance of the chord form the centre is}& \\ \text{(B) Two parallel chords of length 30 cm}& \text{(q) 5.196 cm}\\ \text{And 16 cm. are drawn on the opposite sides}& \\ \text{of the centre}\text{of a circle of radius 17 cm.}& \\ \text{The distance between the chords}& \\ \text{(C) The length of a chords which is at a distance of}& \text{(r) 5.291 cm}\\ \text{4 cm from the centre of the circle of radius 6 cm is}& \\ \text{(D) An equilateral triangle of side 9 cm is inscribed}& \text{(s) 8.94 cm}\\ \text{In a circle. The radius of the circle is}& \\ \text{Choose the correct option:}& \end{array}$

1. A-r; B-p; C-q; D-s

2. A-r; B-p; C-s; D-q

3. A-r; B-s; C-p; D-q

4. A-p; B-q; C-r; D-s

Q. In the given figure, the bisectors of ∠B and ∠C of ∆ABC meet at I. If IP ⊥ BC, IQ ⊥ CA and IR ⊥ AB, prove that (i) IP = IQ = IR, (ii) IA bisects ∠A.

Q.

For what value of $x$ will $△ABC$ be congruent to $△XYZ$ ?

1. $x={50}^{\circ }$
2. $x={40}^{\circ }$
3. $x={30}^{\circ }$
4. $x={60}^{\circ }$

Q.
In fig. 2.41, prove that $△$DEM $~$$△$KNM.
If $\frac{DM}{KM}$ = $\frac{5}{3}$ and KN = 4.5 Find ED.

Q. Which of the following options is/are appropriate criteria for congruence?

1. S.S.S.
2. A.A.A.
3. A.S.A.
4. S.A.S.

Q.

In the triangle ABC

$P^2=Q^2+R^2$

1. 3, 4, 7

2. 8, 15, 17

Q.

In the given figure, if $\angle BAD=\angle CAD,\angle ABD=\angle ACD,$ then which of the following is false?

1. $△ABD\cong △ACD$ by SAS postulate

2. $△ABD\cong △ACD$ by AAS postulate

3. AB = AC

4. BD = CD

Q.

Which of the following tests cannot be undertaken for checking the construction of triangles?

1. SSS Congruency

2. SAS congruency

3. ASA Congruency

4. AAA Congruency

Q. By which congruence rule, △QUT ≅ △QST?

1. 
   ASA
2. 
   AAS

Q. Which of the following is not a criterion for congruence of triangles?

(a) SAS

(b) SSA

(c) ASA

(d) SSS

Q.

In $△ABC$ and $△XZY$, if AB = XZ, BC = ZY and CA = YX, then by which postulate is $△ABC$ congruent to $△XZY$ ?

1. SSS

2. ASA

3. RHS

4. SAS