Question

Below are given the measures of certain sides and angles of triangles. Identify those
which cannot be constructed and say why you
not be constructed and, say why you cannot construct them. Construct rest of
the triangles.
Triangle
Given measurements
| 1. AABC
AB= 5 cm.
m_B= 115º;
mZA= 85°;
2. APQR
QR = 4.7 cm.
mZQ= 30°; mZR= 60°;
3. AABC mZA= 70°; mZB = 50°;
AC = 3 cm.
4. ALMN mZL= 60°; m N = 120°;
LM= 5 cm.
5. AABC
BC = 2 cm;
AB = 4 cm;
AC = 2 cm.
6. APQR
PQ = 3.5 cm.;
QR = 4 cm.; PR = 3.5 cm.
7. AXYZ XY= 3 cm;
YZ= 4 cm;
XZ= 5 cm
8. ADEF
DE = 4.5cm; EF = 5.5cm; DF = 4 cm.​

Answer 1

Given :  Triangle measurements

AB= 5 cm.

m∠B= 115º;

m∠A= 85°;

To Find : Construct or mention the reason why ot can not be constructed

Solution

AB= 5 cm.

m∠B= 115°

m∠A= 85°

Sum of angles of triangle = 180°

m∠A +m ∠B + m∠C  = 180°

=> 85°+  115° +  m∠C  = 180°

=> 200° +  m∠C  = 180°

=> m∠C  =  -20°

Angle of a triangle is always positive hence not possible

so it can not be constructed

ΔABC

BC = 2 cm;

AB = 4 cm;

AC = 2 cm.

sum of two sides of triangles is greater than third side

but 2 + 2 = 4  

Hence Can not be constructed

Please post Question one by one

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Answer 2

Step-by-step explanation:

✰ Question ⤵

| 1. AABC

AB= 5 cm.

m_B= 115º;

mZA= 85°;

✰ To Find ⤵

• Construct or mention the reason why it can not be constructed ?

✰ Solution ⤵

$\sf \: AB = 5cm \\ \sf \: m\angle A = 85° \\ \sf \: m\angle B = 115°$

Sum of angles of triangle = 180°

$\sf m\angle \: A + m\angle B + m\angle \: C = 180°$

$\sf=> 85° + 115° + m \angle C = 180° </p><p> \\ \sf => 200 + m\angle C = 180°</p><p> \\ => \sf m\angle C = 180°</p><p> \\ => \sf \red {m\angle C = -20°}$

Angle of a triangle is always opposite hence not possible so it can not be constructed.

$\sf\triangle ABC$

• AB = 4cm
• AC = 2cm
• BC = 2cm

Sum of two sides of triangle is greater than third side but 2+2 = 4

.

Hence, Triangle can not be constructed

.

.

Hope it helpful✌️

@Somya2563