Question

lesson 4: congruent triangles, part 2
cool down: angles all the way
andre and lin were playing info gap: tmi, using card 3.
andre asked, can i have all 3 angles? lin told andre that one angle was 16°, one angle was 143°, and one angle was 21°. here is the triangle that andre made:

1. is andres triangle congruent to the one on the data card?
2. what other information could andre have asked for to be sure the triangle he drew is congruent?

Explanation:

Step1: Check congruence by angle - side - angle (ASA) or side - angle - side (SAS) etc.

In the first triangle (Data Card), we have angles \(16^{\circ},143^{\circ},21^{\circ}\) and sides \(4,5,8.5\). In Andre's triangle, we only know the angles. For two triangles to be congruent by ASA, we need two angles and the included side; by SAS, two sides and the included angle. Since Andre only has angles, we can't confirm congruence.

Step2: Determine additional information

For ASA: If Andre knew the length of the side between two of the angles (e.g., the side between \(16^{\circ}\) and \(21^{\circ}\) in the Data Card is \(8.5\)). For SAS: If he knew the lengths of two sides and the measure of the included angle (e.g., if he knew that the sides adjacent to the \(16^{\circ}\) angle have lengths \(5\) and \(8.5\))

Answer:

1. No.
2. The length of a side (either the side between two known angles for ASA or two sides and the included angle for SAS).