Question

Geometry? I am really bad at math and have dyscalcullia. Please help.

Answer 1

Answer: The answers are (1). 90°, (2) 2 units, (3) ON, (4) Side-angle-side, (5) A.

Explanation: Based on the attached file, the calculations are as follows:

(1) Since NO is perpendicular to LM, so ∠LON and ∠MON measure 90 degrees.

(2) LO = OM = 2 units.

(3) ΔLON and ΔMON share side ON.

(4) Triangles LON and MON are congruent by the side-angle-side postulate.

(5) The pair of rigid motions that shows that ΔABC and ΔA'B'C' are congruent to each other is

(A) Reflection across the X-axis followed by a translation of 3 units up.

Answer 2

We see from the figure,

1. ∠LON and ∠MON both measure = 90°

2. LO = OM = 2 units

3. ΔLON and ΔMON share the side ON

Since, in both triangles, we have LO=OM, ∠LON = ∠MON and ON=ON.

4. ΔLON and ΔMON are congruent by SAS Postulate

5. We have, ΔABC and ΔA'B'C' are congruent.

It can be seen that, they are congruent by applying the transformations,

Reflection across x-axis followed by translation of 3 units upwards.