Question: 1.1-1.3 Homework POSSIBLE POINTS: 3.33 Refer to the diagram. Starting with 2 marked points, $A$ and $B$, place, in order, the straightedge and compass moves required to construct the triangle $ABC$ in this diagram. Use a straightedge to create segments $AB$, $AC$, $BC$. Mark a point of intersection between the two circles as $C$. Use a compass to create a circle centered at $A$ passing through $B$. Use a compass to create a circle centered at $B$ passing through $A$.

1. **Problem Statement:** Construct triangle $ABC$ given points $A$ and $B$ using straightedge and compass. 2. **Step 1: Draw segment $AB$** Use a straightedge to draw the segment connecting points $A$ and $B$. 3. **Step 2: Draw circle centered at $A$ passing through $B$** Use a compass with center at $A$ and radius $AB$ to draw a circle. 4. **Step 3: Draw circle centered at $B$ passing through $A$** Use a compass with center at $B$ and radius $BA$ to draw another circle. 5. **Step 4: Mark the intersection points of the two circles** The two circles intersect at two points; mark the upper intersection point as $C$. 6. **Step 5: Draw segments $AC$ and $BC$** Use a straightedge to draw segments $AC$ and $BC$. 7. **Result:** Triangle $ABC$ is constructed with sides $AB$, $AC$, and $BC$. This method uses the property that points on the circle centered at $A$ with radius $AB$ are all at distance $AB$ from $A$, and similarly for the circle centered at $B$. Their intersection points are equidistant from $A$ and $B$, forming an isosceles triangle $ABC$.