Question

1. andre is drawing a triangle that is congruent to this one.

he begins by constructing an angle congruent to angle
lkj. what is the least amount of additional information
that andre needs to construct a triangle congruent to
this one?

(from unit 2, lesson 4.)

1. here is a diagram of a straightedge and

compass construction. c is the center of
one circle, and b is the center of the
other. which segment has the same
length as segment ca?
a. ba
b. bd
c. cb
d. ad
(from unit 1, lesson 1.)

Explanation:

Question 6

Step1: Recall congruence criteria

Triangle congruence criteria include ASA (Angle - Side - Angle), SAS (Side - Angle - Side), SSS (Side - Side - Side), AAS (Angle - Angle - Side).

Step2: Analyze the given information

Andre has already constructed one angle (\(\angle LKJ\)). For the least amount of additional information, using the SAS criterion. If we know the lengths of the two sides adjacent to the constructed angle (\(LK\) and \(KJ\)), we can construct a congruent triangle.

Step1: Use the property of circles

Since \(C\) is the center of one circle and \(CA\) is a radius. In a circle, all radii are equal.

Step2: Check each option

• Option A: \(BA\) is not a radius of the circle with center \(C\).
• Option B: \(BD\) is not a radius of the circle with center \(C\).
• Option C: \(CB\) is not a radius of the circle with center \(C\) (it is a radius of the circle with center \(B\) if \(B\) is the center of a circle, but we are looking for the length equal to \(CA\) which is a radius of the circle with center \(C\)). Wait, no, actually, if we consider the construction, \(CA\) and \(CB\) are radii of the same - sized circles (assuming the compass width was set to \(CA\) to draw the arc).
• Option D: \(AD\) is not a radius of the circle with center \(C\).

Answer:

The lengths of the two sides adjacent to \(\angle LKJ\) (i.e., \(LK\) and \(KJ\))

Question 7