Question

12. if EA=4, HE=8, and ER=5. find HT?

13. determine if the sides are proportional. if so prove thag sur ~eup.


please someone help me with both questions!!

Answer 1

HT = 15

Explanation:

HA = HE + EA = 8 + 4

So

EA/HA = ER/HT

HT = HA * ER / EA

HT = 12 * 5/4

HT = 15

Answer

HT = 15

Answer 2

12. HT = 15

13. Ratios are equal and triangles are similar.

Explanation:

Problem 12.

Because of the parallel lines, triangles AER and AHT are similar. EA = 4, and HE = 8. EA + HE = HA = 12.

EA/HA = ER/HT

4/12 = 5/HT

4HT = 12 * 5

HT = 3 * 5

HT = 15

Problem 13.

EU/SU = 6/15 = 2/5

PU/UR = 8/20 = 2/5

Since the ratios above are equal, the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of the other triangle. The included angles are congruent since they are vertical angles. By SAS Similarity, the triangles are similar.