In a quadrilateral $$ \mathrm{ABCD}, \mathrm{AB}=4.7 \mathrm{~cm}, \mathrm{BC}=5.3 \mathrm{~cm}, \mathrm{CD}=6.1 \mathrm{~cm}, \mathrm{AD}=5.9 \mathrm{~cm} $$ and $$ \mathrm{BD}=4.4 \mathrm{~A} $$ (i) Construct a quadrilateral ABCD from the given data: (ii) Measure the length of AC . In a quadrilateral $$ \mathrm{DEFG}, \mathrm{DE}=3.5 \mathrm{~cm}, \mathrm{EF}=6.5 \mathrm{~cm}, \Varangle \mathrm{D}=\Varangle \mathrm{F}=105^{\circ} $$ and $$
ot \subset \mathrm{G}=75^{\circ} $$, (i) Construct a quadrilateral DEFG from the given data: (ii) Measure the unknown sides In a quadrilateral $$ \mathrm{DEFG}, \mathrm{DE}=5.6 \mathrm{~cm}, \mathrm{EF}=4 \mathrm{~cm}, \Varangle \mathrm{D}=40^{\circ}, \Varangle \mathrm{E}=110^{\circ} $$, and $$
ot \boxed{\mathrm{G}}=70^{\circ} $$ (i) Construct a quadrilateral DEFG from the given data: (ii) Measure the unknown sides

Question

In a quadrilateral $$ \mathrm{ABCD}, \mathrm{AB}=4.7 \mathrm{~cm}, \mathrm{BC}=5.3 \mathrm{~cm}, \mathrm{CD}=6.1 \mathrm{~cm}, \mathrm{AD}=5.9 \mathrm{~cm} $$ and $$ \mathrm{BD}=4.4 \mathrm{~A} $$ (i) Construct a quadrilateral ABCD from the given data: (ii) Measure the length of AC . In a quadrilateral $$ \mathrm{DEFG}, \mathrm{DE}=3.5 \mathrm{~cm}, \mathrm{EF}=6.5 \mathrm{~cm}, \Varangle \mathrm{D}=\Varangle \mathrm{F}=105^{\circ} $$ and $$ 
ot \subset \mathrm{G}=75^{\circ} $$, (i) Construct a quadrilateral DEFG from the given data: (ii) Measure the unknown sides In a quadrilateral $$ \mathrm{DEFG}, \mathrm{DE}=5.6 \mathrm{~cm}, \mathrm{EF}=4 \mathrm{~cm}, \Varangle \mathrm{D}=40^{\circ}, \Varangle \mathrm{E}=110^{\circ} $$, and $$ 
ot \boxed{\mathrm{G}}=70^{\circ} $$ (i) Construct a quadrilateral DEFG from the given data: (ii) Measure the unknown sides

UpStudy AI · Accepted Answer

To solve the problem, we will break it down into three parts, each corresponding to the quadrilaterals $$ABCD$$ and $$DEFG$$.

### Quadrilateral ABCD

**Given:**
- $$AB = 4.7 \, 	ext{cm}$$
- $$BC = 5.3 \, 	ext{cm}$$
- $$CD = 6.1 \, 	ext{cm}$$
- $$AD = 5.9 \, 	ext{cm}$$
- $$BD = 4.4 \, 	ext{cm}$$

#### (i) Constructing Quadrilateral ABCD

1. **Draw Line Segment AB:**
   - Draw a line segment $$AB$$ of length $$4.7 \, 	ext{cm}$$.

2. **Construct Point B:**
   - From point $$A$$, use a compass to measure $$5.9 \, 	ext{cm}$$ (length of $$AD$$) and draw an arc to locate point $$D$$.

3. **Construct Point C:**
   - From point $$B$$, measure $$5.3 \, 	ext{cm}$$ (length of $$BC$$) and draw an arc.
   - From point $$D$$, measure $$6.1 \, 	ext{cm}$$ (length of $$CD$$) and draw another arc.
   - The intersection of these two arcs gives point $$C$$.

4. **Connect Points:**
   - Connect points $$A$$, $$B$$, $$C$$, and $$D$$ to form quadrilateral $$ABCD$$.

#### (ii) Measuring Length of AC

To measure the length of $$AC$$, use a ruler to measure the distance between points $$A$$ and $$C$$ after constructing the quadrilateral.

### Quadrilateral DEFG (First Instance)

**Given:**
- $$DE = 3.5 \, 	ext{cm}$$
- $$EF = 6.5 \, 	ext{cm}$$
- $$\angle D = \angle F = 105^\circ$$
- $$\angle G = 75^\circ$$

#### (i) Constructing Quadrilateral DEFG

1. **Draw Line Segment DE:**
   - Draw a line segment $$DE$$ of length $$3.5 \, 	ext{cm}$$.

2. **Construct Angles:**
   - At point $$D$$, use a protractor to measure and draw an angle of $$105^\circ$$ to locate point $$F$$.
   - At point $$E$$, measure and draw another angle of $$105^\circ$$ to locate point $$G$$.

3. **Construct Lengths:**
   - From point $$D$$, measure $$6.5 \, 	ext{cm}$$ to locate point $$F$$.
   - From point $$E$$, measure the distance to locate point $$G$$ based on the angle.

4. **Connect Points:**
   - Connect points $$D$$, $$E$$, $$F$$, and $$G$$ to form quadrilateral $$DEFG$$.

#### (ii) Measuring Unknown Sides

After constructing the quadrilateral, measure the lengths of the unknown sides $$DG$$ and $$EG$$ using a ruler.

### Quadrilateral DEFG (Second Instance)

**Given:**
- $$DE = 5.6 \, 	ext{cm}$$
- $$EF = 4 \, 	ext{cm}$$
- $$\angle D = 40^\circ$$
- $$\angle E = 110^\circ$$
- $$\angle G = 70^\circ$$

#### (i) Constructing Quadrilateral DEFG

1. **Draw Line Segment DE:**
   - Draw a line segment $$DE$$ of length $$5.6 \, 	ext{cm}$$.

2. **Construct Angles:**
   - At point $$D$$, use a protractor to measure and draw an angle of $$40^\circ$$ to locate point $$F$$.
   - At point $$E$$, measure and draw an angle of $$110^\circ$$ to locate point $$G$$.

3. **Construct Lengths:**
   - From point $$D$$, measure $$4 \, 	ext{cm}$$ to locate point $$F$$.
   - From point $$E$$, measure the distance to locate point $$G$$ based on the angle.

4. **Connect Points:**
   - Connect points $$D$$, $$E$$, $$F$$, and $$G$$ to form quadrilateral $$DEFG$$.

#### (ii) Measuring Unknown Sides

After constructing the quadrilateral, measure the lengths of the unknown sides $$DG$$ and $$EG$$ using a ruler.

### Summary

- For each quadrilateral, the construction involves drawing the specified lengths and angles accurately.
- The measurement of unknown sides can be done using a ruler after the construction is complete.

If you need further assistance with specific calculations or measurements, please let me know!
To construct the quadrilaterals ABCD and DEFG, follow these steps: 1. **Quadrilateral ABCD:** - Draw $$AB = 4.7 \, 	ext{cm}$$. - From $$A$$, draw $$AD = 5.9 \, 	ext{cm}$$ to locate $$D$$. - From $$B$$, draw $$BC = 5.3 \, 	ext{cm}$$ and from $$D$$, draw $$CD = 6.1 \, 	ext{cm}$$ to locate $$C$$. - Connect $$A$$, $$B$$, $$C$$, and $$D$$ to form ABCD. - Measure $$AC$$ with a ruler. 2. **Quadrilateral DEFG (First Instance):** - Draw $$DE = 3.5 \, 	ext{cm}$$. - At $$D$$, draw $$\angle D = 105^\circ$$ to locate $$F$$. - At $$E$$, draw $$\angle E = 105^\circ$$ to locate $$G$$. - Measure $$EF = 6.5 \, 	ext{cm}$$ to locate $$F$$. - Connect $$D$$, $$E$$, $$F$$, and $$G$$ to form DEFG. - Measure the unknown sides $$DG$$ and $$EG$$. 3. **Quadrilateral DEFG (Second Instance):** - Draw $$DE = 5.6 \, 	ext{cm}$$. - At $$D$$, draw $$\angle D = 40^\circ$$ to locate $$F$$. - At $$E$$, draw $$\angle E = 110^\circ$$ to locate $$G$$. - Measure $$EF = 4 \, 	ext{cm}$$ to locate $$F$$. - Connect $$D$$, $$E$$, $$F$$, and $$G$$ to form DEFG. - Measure the unknown sides $$DG$$ and $$EG$$. After constructing each quadrilateral, use a ruler to measure the lengths of the specified sides.

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