Question
13 in.
Brock
J
9 in.
Sarah
9 in.
13 in.
K
ILEKS, IKEJI 1
Brock and Sarah are twins. For their birthday, they make a rectangular sheet cake that is 9 inches by 13 inches. They decide to cut the cake into two large pieces so that they will each get exactly the same amount of cake. Sarah suggests that they cut the cake along its diagonal. Brock is not sure whether this will be fair.
Use the SSS Congruence Theorem to help convince Brock that Sarah's suggestion is fair.
L
MULTIPLE-CHOICE QUESTION
What side would Sarah and Brock be sharing?
Segment IJ
I
Segment JK
Segment IK
Brock
J
9 in.
Sarah
9 in.
13 in.
K
ILEKS, IKEJI 1
Brock and Sarah are twins. For their birthday, they make a rectangular sheet cake that is 9 inches by 13 inches. They decide to cut the cake into two large pieces so that they will each get exactly the same amount of cake. Sarah suggests that they cut the cake along its diagonal. Brock is not sure whether this will be fair.
Use the SSS Congruence Theorem to help convince Brock that Sarah's suggestion is fair.
L
MULTIPLE-CHOICE QUESTION
What side would Sarah and Brock be sharing?
Segment IJ
I
Segment JK
Segment IK
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine whether the cut along the diagonal will result in two equal pieces of cake, we can use the SSS (Side-Side-Side) Congruence Theorem.
1. **Diagram**: Consider the rectangular cake with corners labeled:
- \( I \) (top left corner)
- \( J \) (top right corner)
- \( K \) (bottom right corner)
- \( L \) (bottom left corner)
The dimensions provided are:
- Length \( IJ = 9 \) inches (height)
- Length \( JK = 13 \) inches (width)
2. **Diagonal Cut**: If Sarah suggests cutting the cake along the diagonal \( IK \), we will have two triangles: \(\triangle IJK\) and \(\triangle ILK\).
3. **Comparing the Triangles**:
- **For Triangle IJK**:
- Side \( IJ = 9 \) inches
- Side \( JK = 13 \) inches
- Side \( IK \) can be found using the Pythagorean theorem:
\[ IK = \sqrt{IJ^2 + JK^2} = \sqrt{9^2 + 13^2} = \sqrt{81 + 169} = \sqrt{250} = 5\sqrt{10} \, \text{inches} \]
- **For Triangle ILK**:
- Side \( IL = 9 \) inches (height)
- Side \( LK = 13 \) inches (width)
- Side \( IK \) (the diagonal cut already calculated) is still \( 5\sqrt{10} \) inches.
4. **SSS Congruence**:
- Since both triangles share the same side \( IK \) and have the same lengths \( IJ = IL = 9 \) inches and \( JK = LK = 13 \) inches.
- Therefore, by the SSS Congruence Theorem, we conclude that \(\triangle IJK \cong \triangle ILK\).
Since these two triangles are congruent, the areas will also be equal. This shows that each twin will get exactly the same amount of cake, which confirms to Brock that cutting along the diagonal is indeed a fair way to slice the cake.
**Answer to the Multiple-Choice Question**: The side that Sarah and Brock would be sharing is **Segment IK**.
1. **Diagram**: Consider the rectangular cake with corners labeled:
- \( I \) (top left corner)
- \( J \) (top right corner)
- \( K \) (bottom right corner)
- \( L \) (bottom left corner)
The dimensions provided are:
- Length \( IJ = 9 \) inches (height)
- Length \( JK = 13 \) inches (width)
2. **Diagonal Cut**: If Sarah suggests cutting the cake along the diagonal \( IK \), we will have two triangles: \(\triangle IJK\) and \(\triangle ILK\).
3. **Comparing the Triangles**:
- **For Triangle IJK**:
- Side \( IJ = 9 \) inches
- Side \( JK = 13 \) inches
- Side \( IK \) can be found using the Pythagorean theorem:
\[ IK = \sqrt{IJ^2 + JK^2} = \sqrt{9^2 + 13^2} = \sqrt{81 + 169} = \sqrt{250} = 5\sqrt{10} \, \text{inches} \]
- **For Triangle ILK**:
- Side \( IL = 9 \) inches (height)
- Side \( LK = 13 \) inches (width)
- Side \( IK \) (the diagonal cut already calculated) is still \( 5\sqrt{10} \) inches.
4. **SSS Congruence**:
- Since both triangles share the same side \( IK \) and have the same lengths \( IJ = IL = 9 \) inches and \( JK = LK = 13 \) inches.
- Therefore, by the SSS Congruence Theorem, we conclude that \(\triangle IJK \cong \triangle ILK\).
Since these two triangles are congruent, the areas will also be equal. This shows that each twin will get exactly the same amount of cake, which confirms to Brock that cutting along the diagonal is indeed a fair way to slice the cake.
**Answer to the Multiple-Choice Question**: The side that Sarah and Brock would be sharing is **Segment IK**.
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