Which of These Triangles Appears Not to Be Congruent

September 18, 2022 admin 108 Views

Mathematics NCERT Form 7, Chapter seven:Congruence of Triangles– The chapter focuses on thecongruency of plane figures,line segments,angles, andtriangles.

Congruent objects
are verbal
copies
of i another.

The first section of the chapter deals withcongruence of plane figures, congruence among line segments
and
congruence of angles.

If two
line segments
have the same (i.e., equal) length, they are
coinciding. Also, if two
line segments are congruent, they have the same length.
If two
angles
have the
same measure,
they are
congruent.
As well, if two
angles are congruent, their measures are same.

Afterward that,congruence of trianglesis discussed. Practice 7.1 is based on the concept of above cited topics. The other one-half of the chapter deals withCriteria For the congruence of Triangles. Caption of criterion is given in an interesting way, they are mentioned in the class of games. Students will be briefed about the following criterion:
1.SSS congruence criteria:
Triangles are
congruent
if
3 sides
of the 1 are equal to the
three respective sides
of the other.
2.SAS congruence criteria:
Triangles are
congruent
if
two sides
and the
angle
included betwixt them in one of the triangle are equal to the
corresponding sides
and the
bending
included between them of the other triangle.
3.ASA congruence criteria:
Two
triangles
are
congruent
if 2
angles
and the
side
included between them in one of the
triangles
are equal to the
corresponding angles and the side
included between them of the other triangle.
Emphasis will likewise be laid upon the topic- Congruence Among Right-Angled Triangles.
RHS congruence criteria:
If nether a correspondence, the
hypotenuse
and
one side of a correct-angled triangle
are respectively equal to the
hypotenuse and one side of another
correct-angled triangle,
then the triangles are
coinciding.

Later the affiliateCongruence of Trianglesconcludes with a summary.

Page No 137:

Question 1:

Consummate the following statements:

(a) Two line segments are congruent if __________.

(b) Among ii coinciding angles, ane has a measure out of 70°; the measure of the other angle is __________.

Answer:

(a) They take the same length

(b) 70°

Page No 137:

Question ii:

Give any two real-life examples for congruent shapes.

Answer:

(i) Sheets of same letter pad

(ii) Biscuits in the same bundle

Page No 137:

Question 3:

If ΔABC ≅ ΔFED nether the correspondence ABC ↔ FED, write all the Corresponding congruent parts of the triangles.

Answer:

If these triangles are congruent, then the respective angles and sides will exist equal to each other.

∠A ↔ ∠F

∠B ↔ ∠E

∠C ↔ ∠D

Page No 137:

Question 4:

If ΔDEF ≅ ΔBCA, write the role(s) of ΔBCA that correspond to

(i) ∠E (ii)

(iii) ∠F (iv)

Answer:

(i) ∠C

(two)

(iii) ∠A

(iv)

Video Solution for congruence of triangles (Page: 137 , Q.No.: 4)

NCERT Solution for Class seven math – congruence of triangles 137 , Question 4

Page No 149:

Question 1:

Which congruence criterion practice you use in the post-obit?

(a)
Given:
AC = DF

AB = DE

BC = EF

So, ΔABC ≅ ΔDEF

(b)
Given:
ZX = RP

RQ = ZY

∠PRQ = ∠XZY

And then, ΔPQR ≅ ΔXYZ

∠NML = ∠GFH

ML = FG

So, ΔLMN ≅ ΔGFH

(d)
Given:
EB = DB

AE = BC

∠A = ∠C = xc°

So, ΔABE ≅ ΔCDB

Respond:

(a) SSS, as the sides of ΔABC are equal to the sides of ΔDEF.

(b) SAS, as 2 sides and the bending included between these sides of ΔPQR are equal to 2 sides and the angle included betwixt these sides of ΔXYZ.

(c) ASA, as two angles and the side included between these angles of ΔLMN are equal to 2 angles and the side included between these angles of ΔGFH.

(d) RHS, as in the given two right-angled triangles, one side and the hypotenuse are respectively equal.

Page No 149:

Question 2:

Yous want to show that ΔART ≅ ΔPEN,

(a) If you take to apply SSS criterion, then you need to show

(i) AR = (two) RT = (three) AT =

(b) If it is given that ∠T = ∠N and y’all are to employ SAS benchmark, you lot need to have

(i) RT = and (ii) PN =

(i) ? (ii) ?

Answer:

(a)

(i) AR = PE

(two) RT = EN

(iii) AT = PN

(b)

(i) RT = EN

(ii) PN = AT

(c)

(i) ∠ATR = ∠PNE

(ii) ∠RAT = ∠EPN

Video Solution for congruence of triangles (Page: 149 , Q.No.: 2)

NCERT Solution for Class 7 math – congruence of triangles 149 , Question 2

Page No 150:

Question 3:

You have to show that ΔAMP ≅ AMQ.

In the following proof, supply the missing reasons.

–	Steps	–	Reasons
(i)	PM = QM	(i)	…
(two)	∠PMA = ∠QMA	(ii)	…
(three)	AM = AM	(3)	…
(iv)	ΔAMP ≅ ΔAMQ	(4)	…

Answer:

(i) Given

(two) Given

(3) Common

(four) SAS, every bit the ii sides and the angle included between these sides of ΔAMP are equal to two sides and the angle included between these sides of ΔAMQ.

Page No 150:

Question 4:

In ΔABC, ∠A = xxx°, ∠B = twoscore° and ∠C = 110°

In ΔPQR, ∠P = 30°, ∠Q = twoscore° and ∠R = 110°

A student says that ΔABC ≅ ΔPQR by AAA congruence criterion. Is he justified? Why or why non?

Answer:

No. This property represents that these triangles accept their respective angles of equal measure. However, this gives no information about their sides. The sides of these triangles take a ratio somewhat different than i:1. Therefore, AAA holding does non prove the 2 triangles congruent.

Page No 150:

Question 5:

In the figure, the two triangles are coinciding.

The respective parts are marked. We can write ΔRAT ≅ ?

Answer:

It tin exist observed that,

∠RAT = ∠WON

∠Fine art = ∠Own

AR = OW

Therefore, ΔRAT

ΔWON, past ASA criterion.

Video Solution for congruence of triangles (Page: 150 , Q.No.: 5)

NCERT Solution for Class 7 math – congruence of triangles 150 , Question five

Folio No 150:

Question 6:

Complete the congruence statement:

ΔBCA ≅?

ΔQRS ≅?

Answer:

Given that, BC = BT

TA = CA

BA is common.

Therefore, ΔBCA

ΔBTA

Similarly, PQ = RS

TQ = QS
PT = RQ

Therefore, ΔQRS

ΔTPQ

Folio No 150:

Question seven:

In a squared sail, depict ii triangles of equal areas such that

(i) The triangles are congruent.

(ii) The triangles are non coinciding.

What can you lot say about their perimeters?

Answer:

(i)

Hither, ΔABC and ΔPQR have the same area and are congruent to each other besides. Also, the perimeter of both the triangles will exist the same.

(ii)

Hither, the two triangles have the aforementioned elevation and base of operations. Thus, their areas are equal. However, these triangles are not congruent to each other. Also, the perimeter of both the triangles will not be the same.

Video Solution for congruence of triangles (Page: 150 , Q.No.: 7)

NCERT Solution for Form 7 math – congruence of triangles 150 , Question 7

Folio No 150:

Question 8:

Draw a rough sketch of ii triangles such that they have 5 pairs of coinciding parts only still the triangles are non congruent.

Answer:

Consider two triangles

△

ABC and

△

XYZ.

△

ABC and

△

XYZ,

∠ A = ∠ Ten = 40 ° ∠ B = ∠ Y = 80 ° ∠ C = ∠ Z = 60 ° AB = YZ AC = XY

The given triangles have v pairs of congruent parts. Just these two triangles are non congruent by any benchmark of congruence.

Page No 150:

Question nine:

If ΔABC and ΔPQR are to be coinciding, name ane additional pair of corresponding parts. What criterion did you use?

Reply:

BC = QR

ΔABC

ΔPQR (ASA criterion)

Folio No 151:

Question 10:

Explain, why

ΔABC ≅ ΔFED

Answer:

Given that, ∠ABC = ∠FED (i)

∠BAC = ∠EFD (two)

The two angles of ΔABC are equal to the 2 respective angles of ΔFED. Also, the sum of all interior angles of a triangle is 180º. Therefore, third bending of both triangles will also be equal in measure.

∠BCA = ∠EDF (three)

Also, given that, BC = ED (4)

By using equation (1), (3), and (4), we obtain

ΔABC ≅ ΔFED (ASA criterion)

Video Solution for congruence of triangles (Page: 151 , Q.No.: 10)

NCERT Solution for Form 7 math – congruence of triangles 151 , Question 10

View NCERT Solutions for all chapters of Course seven