Question: User: Say bisector!
Lesson 1-5 Jigsaw Construction Review
Name: Daylyl Mays Period: 7°
Name: __________ Period: _________
Exit Ticket
1.
Is point E
a. Closer to A
b. Closer to B
c. Equidistant to A and B
Is point D
a. Closer to A
b. Closer to B
c. Equidistant to A and B
Why for both?
2.
Which is not necessarily true?
a. AC = BP
b. AB = BQ
c. AB = BP
d. BP = PQ
Why?
3.
Is triangle ABC
a. Equilateral
b. Isosceles
c. Neither
Is triangle AFG
a. Equilateral
b. Isosceles
c. Neither
Why?
4. Jericho wants to construct an equilateral quadrilateral, called a rhombus. It's not regular, because the angles are not all the same. The instructions below are a good start. Complete them and then add the last step.
Draw the circle centered at point C with radius CD.
Draw the circle centered at point D with radius DC.
Label the intersections of circles as points E and F.
Draw lines between the points
I know this is a rhombus, because ______________________
Make a conjecture about the angles in the rhombus:
If are equal, c 30 are not.
Position hints:
top-left: point E is closer to A than B; point D is equidistant to A and B; coordinate graph with points A and B on the x-axis, C above the x-axis, D below, E left of the y-axis, and F near the lower center.
center: two overlapping circles with points A, B, C, P, Q; shaded triangles A C B and B P Q; BP = PQ is not necessarily true.
top-right: diagram of concentric circles with triangle ABC and triangle AFG; triangle ABC is neither, triangle AFG is isosceles.
1. **Problem:** Determine the relative distances of points E and D to points A and B.
- Given: Point E is closer to A than B.
- Given: Point D is equidistant to A and B.
**Explanation:**
- If a point is equidistant from two points, it lies on the perpendicular bisector of the segment connecting those points.
2. **Problem:** Identify which equality is not necessarily true among the given segments.
- Options:
a. $AC = BP$
b. $AB = BQ$
c. $AB = BP$
d. $BP = PQ$
**Explanation:**
- Without additional information, $BP = PQ$ is not necessarily true because these segments depend on specific constructions.
3. **Problem:** Classify triangles $ABC$ and $AFG$.
- Triangle $ABC$ is neither equilateral nor isosceles.
- Triangle $AFG$ is isosceles.
**Explanation:**
- Equilateral triangles have all sides equal.
- Isosceles triangles have at least two sides equal.
4. **Problem:** Construct a rhombus and explain why it is a rhombus.
- Steps:
1. Draw the circle centered at point $C$ with radius $CD$.
2. Draw the circle centered at point $D$ with radius $DC$.
3. Label the intersections of circles as points $E$ and $F$.
4. Draw lines between the points to form the quadrilateral.
- **Reasoning:**
- A rhombus has all sides equal in length.
- Since $CE = CD = DF = FC$ (radii of the circles), all sides are equal.
- **Conjecture about angles:**
- Opposite angles in a rhombus are equal.
- Adjacent angles are supplementary but not necessarily equal.
**Final answer:**
- Point $E$ is closer to $A$ than $B$.
- Point $D$ is equidistant to $A$ and $B$.
- $BP = PQ$ is not necessarily true.
- Triangle $ABC$ is neither equilateral nor isosceles.
- Triangle $AFG$ is isosceles.
- The quadrilateral formed by points $C, D, E, F$ is a rhombus because all sides are equal.