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What can you conclude by using the given statement together with each additional statement? If no conclusion is possible, say so.

Given: Every square is a rhombus.

a. ABCD is a rhombus.

b. In quad. LAST, LALT.

c. PQRS is a square.

d. GHIJ is not a square.

Short Answer

Expert verified

a. Theconclusion is not possible.

b. LAST, therefore it cannot be square.

c. The conclusion is thatPQRS is a square.

d. The conclusion is not possible.

Step by step solution

01

a.Step 1 – Consider the given statements

The given statement is 鈥淓very square is a rhombus鈥

The given additional statement is 鈥ABCD is a rhombus鈥.

Hence every square is a rhombus doesn鈥檛 imply that every rhombus is a square.

02

– Explanation

ConsiderABCD is a rhombus then it may or may not a square, since every square is a rhombus doesn鈥檛 imply that every rhombus is a square.

03

– Conclusion 

Hence, conclusion is not possible.

04

b.Step 1 – Consider the given statements

The given statement is 鈥淓very square is a rhombus鈥

The given additional statement is 鈥淚n quadrilateral LAST, LALT鈥.

Here LALTimplies that adjacent sides are not equal.

05

– Explanation

Since adjacent sides are not equal in the quadrilateral LAST, therefore it cannot be square.

06

– Conclusion 

Hence, the conclusion is that LAST cannot be square.

07

c.Step 1 – Consider the given statements

The given statement is 鈥淓very square is a rhombus鈥

The given additional statement is 鈥PQRS is a square鈥.

Here PQRSis given that a square.

08

– Explanation

Since every square is a rhombus, therefore PQRS is a square.

09

– Conclusion 

Hence the conclusion is thatPQRS is a square.

10

d.Step 1 – Consider the given statements

The given statement is 鈥淓very square is a rhombus鈥

The given additional statement is 鈥GHIJis not a square鈥.

Here GHIJis given that not a square.

11

– Explanation

Since every square is a rhombus, therefore GHIJ may or may not a rhombus.

12

– Conclusion 

Hence, the conclusion is not possible.

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