2. Both a parallelogram and a kite have two pairs of congruent sides. How are the congruent sides of a kite different from the congruent sides of a parallelogram? 3. Crafts The edges of the kite-shaped glass in the sun catcher are sealed with lead strips. \( J H, \mathrm{KH} \), and \( L H \) are 2.75 inches, and \( M H \) is 5.5 inches. How much lead is needed to seal the edges of the sun catcher? If the craftsperson has two 3 -foot lengths of lead, how many sun catchers can be sealed?

Let's break down the problem step by step. ### Part 2: Differences between the congruent sides of a kite and a parallelogram 1. **Definition of a Parallelogram**: A parallelogram has two pairs of opposite sides that are congruent and parallel. This means that both pairs of sides are equal in length and run parallel to each other. 2. **Definition of a Kite**: A kite has two pairs of adjacent sides that are congruent. This means that each pair of congruent sides is next to each other, forming a shape that is symmetric along one diagonal. 3. **Key Differences**: - In a **parallelogram**, the congruent sides are opposite each other and are parallel. - In a **kite**, the congruent sides are adjacent to each other and are not parallel. ### Part 3: Calculating the amount of lead needed for the sun catcher 1. **Given Measurements**: - \( JH = 2.75 \) inches - \( KH = 2.75 \) inches - \( LH = 2.75 \) inches - \( MH = 5.5 \) inches 2. **Total Length of Lead Needed**: - The total length of lead needed to seal the edges of the sun catcher is the sum of all the edges: \[ \text{Total Length} = JH + KH + LH + MH \] Substituting the values: \[ \text{Total Length} = 2.75 + 2.75 + 2.75 + 5.5 \] 3. **Calculating the Total Length**: Let's calculate the total length of lead needed. 4. **Craftsperson's Lead Supply**: - The craftsperson has two 3-foot lengths of lead. First, we need to convert feet to inches: \[ 3 \text{ feet} = 3 \times 12 = 36 \text{ inches} \] Therefore, two lengths of lead is: \[ 2 \times 36 = 72 \text{ inches} \] 5. **Calculating the Number of Sun Catchers**: - To find out how many sun catchers can be sealed, we will divide the total length of lead available by the total length needed for one sun catcher. Now, let's perform the calculations. ### Step 1: Calculate the total length of lead needed for one sun catcher \[ \text{Total Length} = 2.75 + 2.75 + 2.75 + 5.5 \] ### Step 2: Calculate the number of sun catchers that can be sealed \[ \text{Number of Sun Catchers} = \frac{72}{\text{Total Length}} \] Let's calculate these values. Calculate the value by following steps: - step0: Calculate: \(2.75+2.75+2.75+5.5\) - step1: Write as a multiplication: \(2.75\times 3+5.5\) - step2: Multiply the numbers: \(8.25+5.5\) - step3: Add the numbers: \(13.75\) Calculate or simplify the expression \( 72 / (2.75 + 2.75 + 2.75 + 5.5) \). Calculate the value by following steps: - step0: Calculate: \(\frac{72}{\left(2.75+2.75+2.75+5.5\right)}\) - step1: Remove the parentheses: \(\frac{72}{2.75+2.75+2.75+5.5}\) - step2: Write as a multiplication: \(\frac{72}{2.75\times 3+5.5}\) - step3: Multiply the numbers: \(\frac{72}{8.25+5.5}\) - step4: Add the numbers: \(\frac{72}{13.75}\) - step5: Convert the expressions: \(\frac{72}{\frac{55}{4}}\) - step6: Multiply by the reciprocal: \(72\times \frac{4}{55}\) - step7: Multiply: \(\frac{72\times 4}{55}\) - step8: Multiply: \(\frac{288}{55}\) ### Step 1: Total Length of Lead Needed for One Sun Catcher The total length of lead needed to seal the edges of the sun catcher is: \[ \text{Total Length} = 2.75 + 2.75 + 2.75 + 5.5 = 13.75 \text{ inches} \] ### Step 2: Number of Sun Catchers that Can Be Sealed The craftsperson has a total of 72 inches of lead. To find out how many sun catchers can be sealed, we calculate: \[ \text{Number of Sun Catchers} = \frac{72}{13.75} \approx 5.2 \] Since the craftsperson cannot seal a fraction of a sun catcher, they can seal **5 sun catchers** completely. ### Summary of Results - **Total Length of Lead Needed for One Sun Catcher**: \( 13.75 \) inches - **Number of Sun Catchers that Can Be Sealed**: \( 5 \) sun catchers If you have any further questions or need additional assistance, feel free to ask!